[{"data":1,"prerenderedAt":4967},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Falgebra\u002Fbiquadratische-gleichung":546,"formula-related-de\u002Fformulas\u002Fmath\u002Falgebra\u002Fbiquadratische-gleichung":4954},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":5,"checks":4883,"conditions":4917,"conditionsHtml":4918,"deprecated":4919,"description":4877,"extension":4920,"figure":4919,"figureCaption":4919,"figureHtml":4919,"formulaId":4921,"latex":4922,"latexHtml":4923,"level":4924,"meta":4925,"navigation":4926,"path":4927,"redirectFrom":4928,"related":4929,"seo":4934,"stem":4935,"subject":582,"summary":4936,"tags":4937,"variables":4942,"__hash__":4953},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Falgebra\u002Fbiquadratische-gleichung.md","Biquadratische Gleichung",[550,551,552,553,554],"biquadratische Gleichung lösen","Substitution x² = z","Gleichung vierten Grades","x hoch 4 Gleichung","Resubstitution",{"type":556,"value":557,"toc":4876},"minimark",[558,563,983,1698,1796,1800,2244,2469,2716,2854,2886,3293,3796,3799,4115,4225,4229],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571,572,663,664,724,725,785,786,815,816,978,979,982],"p",{},"Eine ",[568,569,570],"strong",{},"biquadratische Gleichung"," enthält nur die Potenzen ",[573,574,577,607],"span",{"className":575},[576],"katex",[573,578,581],{"className":579},[580],"katex-mathml",[582,583,585],"math",{"xmlns":584},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[586,587,588,602],"semantics",{},[589,590,591],"mrow",{},[592,593,594,598],"msup",{},[595,596,597],"mi",{},"x",[599,600,601],"mn",{},"4",[603,604,606],"annotation",{"encoding":605},"application\u002Fx-tex","x^4",[573,608,612],{"className":609,"ariaHidden":611},[610],"katex-html","true",[573,613,616,621],{"className":614},[615],"base",[573,617],{"className":618,"style":620},[619],"strut","height:0.8141em;",[573,622,625,629],{"className":623},[624],"mord",[573,626,597],{"className":627},[624,628],"mathnormal",[573,630,633],{"className":631},[632],"msupsub",[573,634,637],{"className":635},[636],"vlist-t",[573,638,641],{"className":639},[640],"vlist-r",[573,642,645],{"className":643,"style":620},[644],"vlist",[573,646,648,653],{"style":647},"top:-3.063em;margin-right:0.05em;",[573,649],{"className":650,"style":652},[651],"pstrut","height:2.7em;",[573,654,660],{"className":655},[656,657,658,659],"sizing","reset-size6","size3","mtight",[573,661,601],{"className":662},[624,659],", ",[573,665,667,686],{"className":666},[576],[573,668,670],{"className":669},[580],[582,671,672],{"xmlns":584},[586,673,674,683],{},[589,675,676],{},[592,677,678,680],{},[595,679,597],{},[599,681,682],{},"2",[603,684,685],{"encoding":605},"x^2",[573,687,689],{"className":688,"ariaHidden":611},[610],[573,690,692,695],{"className":691},[615],[573,693],{"className":694,"style":620},[619],[573,696,698,701],{"className":697},[624],[573,699,597],{"className":700},[624,628],[573,702,704],{"className":703},[632],[573,705,707],{"className":706},[636],[573,708,710],{"className":709},[640],[573,711,713],{"className":712,"style":620},[644],[573,714,715,718],{"style":647},[573,716],{"className":717,"style":652},[651],[573,719,721],{"className":720},[656,657,658,659],[573,722,682],{"className":723},[624,659]," und eine Zahl, aber kein ",[573,726,728,747],{"className":727},[576],[573,729,731],{"className":730},[580],[582,732,733],{"xmlns":584},[586,734,735,744],{},[589,736,737],{},[592,738,739,741],{},[595,740,597],{},[599,742,743],{},"3",[603,745,746],{"encoding":605},"x^3",[573,748,750],{"className":749,"ariaHidden":611},[610],[573,751,753,756],{"className":752},[615],[573,754],{"className":755,"style":620},[619],[573,757,759,762],{"className":758},[624],[573,760,597],{"className":761},[624,628],[573,763,765],{"className":764},[632],[573,766,768],{"className":767},[636],[573,769,771],{"className":770},[640],[573,772,774],{"className":773,"style":620},[644],[573,775,776,779],{"style":647},[573,777],{"className":778,"style":652},[651],[573,780,782],{"className":781},[656,657,658,659],[573,783,743],{"className":784},[624,659]," und kein ",[573,787,789,802],{"className":788},[576],[573,790,792],{"className":791},[580],[582,793,794],{"xmlns":584},[586,795,796,800],{},[589,797,798],{},[595,799,597],{},[603,801,597],{"encoding":605},[573,803,805],{"className":804,"ariaHidden":611},[610],[573,806,808,812],{"className":807},[615],[573,809],{"className":810,"style":811},[619],"height:0.4306em;",[573,813,597],{"className":814},[624,628],". Weil ",[573,817,819,858],{"className":818},[576],[573,820,822],{"className":821},[580],[582,823,824],{"xmlns":584},[586,825,826,855],{},[589,827,828,834,838,842,848],{},[592,829,830,832],{},[595,831,597],{},[599,833,601],{},[835,836,837],"mo",{},"=",[835,839,841],{"stretchy":840},"false","(",[592,843,844,846],{},[595,845,597],{},[599,847,682],{},[592,849,850,853],{},[835,851,852],{"stretchy":840},")",[599,854,682],{},[603,856,857],{"encoding":605},"x^4 = (x^2)^2",[573,859,861,908],{"className":860,"ariaHidden":611},[610],[573,862,864,867,896,901,905],{"className":863},[615],[573,865],{"className":866,"style":620},[619],[573,868,870,873],{"className":869},[624],[573,871,597],{"className":872},[624,628],[573,874,876],{"className":875},[632],[573,877,879],{"className":878},[636],[573,880,882],{"className":881},[640],[573,883,885],{"className":884,"style":620},[644],[573,886,887,890],{"style":647},[573,888],{"className":889,"style":652},[651],[573,891,893],{"className":892},[656,657,658,659],[573,894,601],{"className":895},[624,659],[573,897],{"className":898,"style":900},[899],"mspace","margin-right:0.2778em;",[573,902,837],{"className":903},[904],"mrel",[573,906],{"className":907,"style":900},[899],[573,909,911,915,919,948],{"className":910},[615],[573,912],{"className":913,"style":914},[619],"height:1.0641em;vertical-align:-0.25em;",[573,916,841],{"className":917},[918],"mopen",[573,920,922,925],{"className":921},[624],[573,923,597],{"className":924},[624,628],[573,926,928],{"className":927},[632],[573,929,931],{"className":930},[636],[573,932,934],{"className":933},[640],[573,935,937],{"className":936,"style":620},[644],[573,938,939,942],{"style":647},[573,940],{"className":941,"style":652},[651],[573,943,945],{"className":944},[656,657,658,659],[573,946,682],{"className":947},[624,659],[573,949,952,955],{"className":950},[951],"mclose",[573,953,852],{"className":954},[951],[573,956,958],{"className":957},[632],[573,959,961],{"className":960},[636],[573,962,964],{"className":963},[640],[573,965,967],{"className":966,"style":620},[644],[573,968,969,972],{"style":647},[573,970],{"className":971,"style":652},[651],[573,973,975],{"className":974},[656,657,658,659],[573,976,682],{"className":977},[624,659]," ist, kann man sie mit einer ",[568,980,981],{},"Substitution"," auf eine quadratische Gleichung zurückführen:",[984,985,986,1201,1233],"ol",{},[987,988,989,992,993,1051,1052,1082,1083,1051,1141,1200],"li",{},[568,990,991],{},"Substituieren:"," ",[573,994,996,1013],{"className":995},[576],[573,997,999],{"className":998},[580],[582,1000,1001],{"xmlns":584},[586,1002,1003,1011],{},[589,1004,1005],{},[592,1006,1007,1009],{},[595,1008,597],{},[599,1010,682],{},[603,1012,685],{"encoding":605},[573,1014,1016],{"className":1015,"ariaHidden":611},[610],[573,1017,1019,1022],{"className":1018},[615],[573,1020],{"className":1021,"style":620},[619],[573,1023,1025,1028],{"className":1024},[624],[573,1026,597],{"className":1027},[624,628],[573,1029,1031],{"className":1030},[632],[573,1032,1034],{"className":1033},[636],[573,1035,1037],{"className":1036},[640],[573,1038,1040],{"className":1039,"style":620},[644],[573,1041,1042,1045],{"style":647},[573,1043],{"className":1044,"style":652},[651],[573,1046,1048],{"className":1047},[656,657,658,659],[573,1049,682],{"className":1050},[624,659]," durch ",[573,1053,1055,1069],{"className":1054},[576],[573,1056,1058],{"className":1057},[580],[582,1059,1060],{"xmlns":584},[586,1061,1062,1067],{},[589,1063,1064],{},[595,1065,1066],{},"z",[603,1068,1066],{"encoding":605},[573,1070,1072],{"className":1071,"ariaHidden":611},[610],[573,1073,1075,1078],{"className":1074},[615],[573,1076],{"className":1077,"style":811},[619],[573,1079,1066],{"className":1080,"style":1081},[624,628],"margin-right:0.044em;"," ersetzen, ",[573,1084,1086,1103],{"className":1085},[576],[573,1087,1089],{"className":1088},[580],[582,1090,1091],{"xmlns":584},[586,1092,1093,1101],{},[589,1094,1095],{},[592,1096,1097,1099],{},[595,1098,597],{},[599,1100,601],{},[603,1102,606],{"encoding":605},[573,1104,1106],{"className":1105,"ariaHidden":611},[610],[573,1107,1109,1112],{"className":1108},[615],[573,1110],{"className":1111,"style":620},[619],[573,1113,1115,1118],{"className":1114},[624],[573,1116,597],{"className":1117},[624,628],[573,1119,1121],{"className":1120},[632],[573,1122,1124],{"className":1123},[636],[573,1125,1127],{"className":1126},[640],[573,1128,1130],{"className":1129,"style":620},[644],[573,1131,1132,1135],{"style":647},[573,1133],{"className":1134,"style":652},[651],[573,1136,1138],{"className":1137},[656,657,658,659],[573,1139,601],{"className":1140},[624,659],[573,1142,1144,1162],{"className":1143},[576],[573,1145,1147],{"className":1146},[580],[582,1148,1149],{"xmlns":584},[586,1150,1151,1159],{},[589,1152,1153],{},[592,1154,1155,1157],{},[595,1156,1066],{},[599,1158,682],{},[603,1160,1161],{"encoding":605},"z^2",[573,1163,1165],{"className":1164,"ariaHidden":611},[610],[573,1166,1168,1171],{"className":1167},[615],[573,1169],{"className":1170,"style":620},[619],[573,1172,1174,1177],{"className":1173},[624],[573,1175,1066],{"className":1176,"style":1081},[624,628],[573,1178,1180],{"className":1179},[632],[573,1181,1183],{"className":1182},[636],[573,1184,1186],{"className":1185},[640],[573,1187,1189],{"className":1188,"style":620},[644],[573,1190,1191,1194],{"style":647},[573,1192],{"className":1193,"style":652},[651],[573,1195,1197],{"className":1196},[656,657,658,659],[573,1198,682],{"className":1199},[624,659],".",[987,1202,1203,1204,1232],{},"Die quadratische Gleichung für ",[573,1205,1207,1220],{"className":1206},[576],[573,1208,1210],{"className":1209},[580],[582,1211,1212],{"xmlns":584},[586,1213,1214,1218],{},[589,1215,1216],{},[595,1217,1066],{},[603,1219,1066],{"encoding":605},[573,1221,1223],{"className":1222,"ariaHidden":611},[610],[573,1224,1226,1229],{"className":1225},[615],[573,1227],{"className":1228,"style":811},[619],[573,1230,1066],{"className":1231,"style":1081},[624,628]," lösen, z.B. mit der p-q-Formel.",[987,1234,1235,1238,1239,1267,1268,1349,1350],{},[568,1236,1237],{},"Resubstituieren:"," Für jede Lösung ",[573,1240,1242,1255],{"className":1241},[576],[573,1243,1245],{"className":1244},[580],[582,1246,1247],{"xmlns":584},[586,1248,1249,1253],{},[589,1250,1251],{},[595,1252,1066],{},[603,1254,1066],{"encoding":605},[573,1256,1258],{"className":1257,"ariaHidden":611},[610],[573,1259,1261,1264],{"className":1260},[615],[573,1262],{"className":1263,"style":811},[619],[573,1265,1066],{"className":1266,"style":1081},[624,628]," die Gleichung ",[573,1269,1271,1293],{"className":1270},[576],[573,1272,1274],{"className":1273},[580],[582,1275,1276],{"xmlns":584},[586,1277,1278,1290],{},[589,1279,1280,1286,1288],{},[592,1281,1282,1284],{},[595,1283,597],{},[599,1285,682],{},[835,1287,837],{},[595,1289,1066],{},[603,1291,1292],{"encoding":605},"x^2 = z",[573,1294,1296,1340],{"className":1295,"ariaHidden":611},[610],[573,1297,1299,1302,1331,1334,1337],{"className":1298},[615],[573,1300],{"className":1301,"style":620},[619],[573,1303,1305,1308],{"className":1304},[624],[573,1306,597],{"className":1307},[624,628],[573,1309,1311],{"className":1310},[632],[573,1312,1314],{"className":1313},[636],[573,1315,1317],{"className":1316},[640],[573,1318,1320],{"className":1319,"style":620},[644],[573,1321,1322,1325],{"style":647},[573,1323],{"className":1324,"style":652},[651],[573,1326,1328],{"className":1327},[656,657,658,659],[573,1329,682],{"className":1330},[624,659],[573,1332],{"className":1333,"style":900},[899],[573,1335,837],{"className":1336},[904],[573,1338],{"className":1339,"style":900},[899],[573,1341,1343,1346],{"className":1342},[615],[573,1344],{"className":1345,"style":811},[619],[573,1347,1066],{"className":1348,"style":1081},[624,628]," lösen.\n",[1351,1352,1353,1538,1643],"ul",{},[987,1354,1355,1410,1411,1537],{},[573,1356,1358,1378],{"className":1357},[576],[573,1359,1361],{"className":1360},[580],[582,1362,1363],{"xmlns":584},[586,1364,1365,1375],{},[589,1366,1367,1369,1372],{},[595,1368,1066],{},[835,1370,1371],{},">",[599,1373,1374],{},"0",[603,1376,1377],{"encoding":605},"z > 0",[573,1379,1381,1400],{"className":1380,"ariaHidden":611},[610],[573,1382,1384,1388,1391,1394,1397],{"className":1383},[615],[573,1385],{"className":1386,"style":1387},[619],"height:0.5782em;vertical-align:-0.0391em;",[573,1389,1066],{"className":1390,"style":1081},[624,628],[573,1392],{"className":1393,"style":900},[899],[573,1395,1371],{"className":1396},[904],[573,1398],{"className":1399,"style":900},[899],[573,1401,1403,1407],{"className":1402},[615],[573,1404],{"className":1405,"style":1406},[619],"height:0.6444em;",[573,1408,1374],{"className":1409},[624],": zwei Lösungen ",[573,1412,1414,1438],{"className":1413},[576],[573,1415,1417],{"className":1416},[580],[582,1418,1419],{"xmlns":584},[586,1420,1421,1435],{},[589,1422,1423,1425,1427,1430],{},[595,1424,597],{},[835,1426,837],{},[835,1428,1429],{},"±",[1431,1432,1433],"msqrt",{},[595,1434,1066],{},[603,1436,1437],{"encoding":605},"x = \\pm\\sqrt{z}",[573,1439,1441,1459],{"className":1440,"ariaHidden":611},[610],[573,1442,1444,1447,1450,1453,1456],{"className":1443},[615],[573,1445],{"className":1446,"style":811},[619],[573,1448,597],{"className":1449},[624,628],[573,1451],{"className":1452,"style":900},[899],[573,1454,837],{"className":1455},[904],[573,1457],{"className":1458,"style":900},[899],[573,1460,1462,1466,1469],{"className":1461},[615],[573,1463],{"className":1464,"style":1465},[619],"height:1.04em;vertical-align:-0.2397em;",[573,1467,1429],{"className":1468},[624],[573,1470,1473],{"className":1471},[624,1472],"sqrt",[573,1474,1477,1528],{"className":1475},[636,1476],"vlist-t2",[573,1478,1480,1523],{"className":1479},[640],[573,1481,1484,1500],{"className":1482,"style":1483},[644],"height:0.8003em;",[573,1485,1489,1493],{"className":1486,"style":1488},[1487],"svg-align","top:-3em;",[573,1490],{"className":1491,"style":1492},[651],"height:3em;",[573,1494,1497],{"className":1495,"style":1496},[624],"padding-left:0.833em;",[573,1498,1066],{"className":1499,"style":1081},[624,628],[573,1501,1503,1506],{"style":1502},"top:-2.7603em;",[573,1504],{"className":1505,"style":1492},[651],[573,1507,1511],{"className":1508,"style":1510},[1509],"hide-tail","min-width:0.853em;height:1.08em;",[1512,1513,1519],"svg",{"xmlns":1514,"width":1515,"height":1516,"viewBox":1517,"preserveAspectRatio":1518},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1520,1521],"path",{"d":1522},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[573,1524,1527],{"className":1525},[1526],"vlist-s","​",[573,1529,1531],{"className":1530},[640],[573,1532,1535],{"className":1533,"style":1534},[644],"height:0.2397em;",[573,1536],{},",",[987,1539,1540,1591,1592,1537],{},[573,1541,1543,1561],{"className":1542},[576],[573,1544,1546],{"className":1545},[580],[582,1547,1548],{"xmlns":584},[586,1549,1550,1558],{},[589,1551,1552,1554,1556],{},[595,1553,1066],{},[835,1555,837],{},[599,1557,1374],{},[603,1559,1560],{"encoding":605},"z = 0",[573,1562,1564,1582],{"className":1563,"ariaHidden":611},[610],[573,1565,1567,1570,1573,1576,1579],{"className":1566},[615],[573,1568],{"className":1569,"style":811},[619],[573,1571,1066],{"className":1572,"style":1081},[624,628],[573,1574],{"className":1575,"style":900},[899],[573,1577,837],{"className":1578},[904],[573,1580],{"className":1581,"style":900},[899],[573,1583,1585,1588],{"className":1584},[615],[573,1586],{"className":1587,"style":1406},[619],[573,1589,1374],{"className":1590},[624],": die Lösung ",[573,1593,1595,1613],{"className":1594},[576],[573,1596,1598],{"className":1597},[580],[582,1599,1600],{"xmlns":584},[586,1601,1602,1610],{},[589,1603,1604,1606,1608],{},[595,1605,597],{},[835,1607,837],{},[599,1609,1374],{},[603,1611,1612],{"encoding":605},"x = 0",[573,1614,1616,1634],{"className":1615,"ariaHidden":611},[610],[573,1617,1619,1622,1625,1628,1631],{"className":1618},[615],[573,1620],{"className":1621,"style":811},[619],[573,1623,597],{"className":1624},[624,628],[573,1626],{"className":1627,"style":900},[899],[573,1629,837],{"className":1630},[904],[573,1632],{"className":1633,"style":900},[899],[573,1635,1637,1640],{"className":1636},[615],[573,1638],{"className":1639,"style":1406},[619],[573,1641,1374],{"className":1642},[624],[987,1644,1645,1697],{},[573,1646,1648,1667],{"className":1647},[576],[573,1649,1651],{"className":1650},[580],[582,1652,1653],{"xmlns":584},[586,1654,1655,1664],{},[589,1656,1657,1659,1662],{},[595,1658,1066],{},[835,1660,1661],{},"\u003C",[599,1663,1374],{},[603,1665,1666],{"encoding":605},"z \u003C 0",[573,1668,1670,1688],{"className":1669,"ariaHidden":611},[610],[573,1671,1673,1676,1679,1682,1685],{"className":1672},[615],[573,1674],{"className":1675,"style":1387},[619],[573,1677,1066],{"className":1678,"style":1081},[624,628],[573,1680],{"className":1681,"style":900},[899],[573,1683,1661],{"className":1684},[904],[573,1686],{"className":1687,"style":900},[899],[573,1689,1691,1694],{"className":1690},[615],[573,1692],{"className":1693,"style":1406},[619],[573,1695,1374],{"className":1696},[624],": keine reelle Lösung.",[564,1699,1700,1701,1729,1730,1758,1759,1795],{},"Eine biquadratische Gleichung hat deshalb höchstens vier reelle Lösungen. Sie liegen symmetrisch zur ",[573,1702,1704,1717],{"className":1703},[576],[573,1705,1707],{"className":1706},[580],[582,1708,1709],{"xmlns":584},[586,1710,1711,1715],{},[589,1712,1713],{},[599,1714,1374],{},[603,1716,1374],{"encoding":605},[573,1718,1720],{"className":1719,"ariaHidden":611},[610],[573,1721,1723,1726],{"className":1722},[615],[573,1724],{"className":1725,"style":1406},[619],[573,1727,1374],{"className":1728},[624],", weil mit ",[573,1731,1733,1746],{"className":1732},[576],[573,1734,1736],{"className":1735},[580],[582,1737,1738],{"xmlns":584},[586,1739,1740,1744],{},[589,1741,1742],{},[595,1743,597],{},[603,1745,597],{"encoding":605},[573,1747,1749],{"className":1748,"ariaHidden":611},[610],[573,1750,1752,1755],{"className":1751},[615],[573,1753],{"className":1754,"style":811},[619],[573,1756,597],{"className":1757},[624,628]," auch ",[573,1760,1762,1779],{"className":1761},[576],[573,1763,1765],{"className":1764},[580],[582,1766,1767],{"xmlns":584},[586,1768,1769,1776],{},[589,1770,1771,1774],{},[835,1772,1773],{},"−",[595,1775,597],{},[603,1777,1778],{"encoding":605},"-x",[573,1780,1782],{"className":1781,"ariaHidden":611},[610],[573,1783,1785,1789,1792],{"className":1784},[615],[573,1786],{"className":1787,"style":1788},[619],"height:0.6667em;vertical-align:-0.0833em;",[573,1790,1773],{"className":1791},[624],[573,1793,597],{"className":1794},[624,628]," eine Lösung ist.",[559,1797,1799],{"id":1798},"beispiele","Beispiele",[573,1801,1804],{"className":1802},[1803],"katex-display",[573,1805,1807,1902],{"className":1806},[576],[573,1808,1810],{"className":1809},[580],[582,1811,1813],{"xmlns":584,"display":1812},"block",[586,1814,1815,1899],{},[589,1816,1817,1823,1825,1828,1834,1837,1840,1842,1844,1848,1877,1879,1885,1887,1889,1891,1893,1895,1897],{},[592,1818,1819,1821],{},[595,1820,597],{},[599,1822,601],{},[835,1824,1773],{},[599,1826,1827],{},"13",[592,1829,1830,1832],{},[595,1831,597],{},[599,1833,682],{},[835,1835,1836],{},"+",[599,1838,1839],{},"36",[835,1841,837],{},[599,1843,1374],{},[1845,1846,1847],"mtext",{},"  ",[1849,1850,1851,1855],"mover",{},[835,1852,1854],{"stretchy":611,"minsize":1853},"3.0em","→",[1856,1857,1860],"mpadded",{"width":1858,"lspace":1859},"+0.6em","0.3em",[589,1861,1862,1865,1867,1869,1875],{},[1845,1863,1864],{}," ",[595,1866,1066],{},[835,1868,837],{},[592,1870,1871,1873],{},[595,1872,597],{},[599,1874,682],{},[1845,1876,1864],{},[1845,1878,1847],{},[592,1880,1881,1883],{},[595,1882,1066],{},[599,1884,682],{},[835,1886,1773],{},[599,1888,1827],{},[595,1890,1066],{},[835,1892,1836],{},[599,1894,1839],{},[835,1896,837],{},[599,1898,1374],{},[603,1900,1901],{"encoding":605},"x^4 - 13x^2 + 36 = 0 \\;\\xrightarrow{\\ z = x^2\\ }\\; z^2 - 13z + 36 = 0",[573,1903,1905,1954,2001,2019,2151,2195,2217,2235],{"className":1904,"ariaHidden":611},[610],[573,1906,1908,1912,1943,1947,1951],{"className":1907},[615],[573,1909],{"className":1910,"style":1911},[619],"height:0.9474em;vertical-align:-0.0833em;",[573,1913,1915,1918],{"className":1914},[624],[573,1916,597],{"className":1917},[624,628],[573,1919,1921],{"className":1920},[632],[573,1922,1924],{"className":1923},[636],[573,1925,1927],{"className":1926},[640],[573,1928,1931],{"className":1929,"style":1930},[644],"height:0.8641em;",[573,1932,1934,1937],{"style":1933},"top:-3.113em;margin-right:0.05em;",[573,1935],{"className":1936,"style":652},[651],[573,1938,1940],{"className":1939},[656,657,658,659],[573,1941,601],{"className":1942},[624,659],[573,1944],{"className":1945,"style":1946},[899],"margin-right:0.2222em;",[573,1948,1773],{"className":1949},[1950],"mbin",[573,1952],{"className":1953,"style":1946},[899],[573,1955,1957,1960,1963,1992,1995,1998],{"className":1956},[615],[573,1958],{"className":1959,"style":1911},[619],[573,1961,1827],{"className":1962},[624],[573,1964,1966,1969],{"className":1965},[624],[573,1967,597],{"className":1968},[624,628],[573,1970,1972],{"className":1971},[632],[573,1973,1975],{"className":1974},[636],[573,1976,1978],{"className":1977},[640],[573,1979,1981],{"className":1980,"style":1930},[644],[573,1982,1983,1986],{"style":1933},[573,1984],{"className":1985,"style":652},[651],[573,1987,1989],{"className":1988},[656,657,658,659],[573,1990,682],{"className":1991},[624,659],[573,1993],{"className":1994,"style":1946},[899],[573,1996,1836],{"className":1997},[1950],[573,1999],{"className":2000,"style":1946},[899],[573,2002,2004,2007,2010,2013,2016],{"className":2003},[615],[573,2005],{"className":2006,"style":1406},[619],[573,2008,1839],{"className":2009},[624],[573,2011],{"className":2012,"style":900},[899],[573,2014,837],{"className":2015},[904],[573,2017],{"className":2018,"style":900},[899],[573,2020,2022,2026,2029,2032,2035,2145,2148],{"className":2021},[615],[573,2023],{"className":2024,"style":2025},[619],"height:1.2569em;vertical-align:-0.011em;",[573,2027,1374],{"className":2028},[624],[573,2030],{"className":2031,"style":900},[899],[573,2033],{"className":2034,"style":900},[899],[573,2036,2039],{"className":2037},[904,2038],"x-arrow",[573,2040,2042,2136],{"className":2041},[636,1476],[573,2043,2045,2133],{"className":2044},[640],[573,2046,2049,2114],{"className":2047,"style":2048},[644],"height:1.2459em;",[573,2050,2052,2055],{"style":2051},"top:-3.322em;",[573,2053],{"className":2054,"style":652},[651],[573,2056,2059],{"className":2057},[656,657,658,659,2058],"x-arrow-pad",[573,2060,2062,2068,2071,2074,2108],{"className":2061},[624,659],[573,2063,2065],{"className":2064},[899,659],[573,2066,1864],{"className":2067},[659],[573,2069,1066],{"className":2070,"style":1081},[624,628,659],[573,2072,837],{"className":2073},[904,659],[573,2075,2077,2080],{"className":2076},[624,659],[573,2078,597],{"className":2079},[624,628,659],[573,2081,2083],{"className":2082},[632],[573,2084,2086],{"className":2085},[636],[573,2087,2089],{"className":2088},[640],[573,2090,2093],{"className":2091,"style":2092},[644],"height:0.8913em;",[573,2094,2096,2100],{"style":2095},"top:-2.931em;margin-right:0.0714em;",[573,2097],{"className":2098,"style":2099},[651],"height:2.5em;",[573,2101,2105],{"className":2102},[656,2103,2104,659],"reset-size3","size1",[573,2106,682],{"className":2107},[624,659],[573,2109,2111],{"className":2110},[899,659],[573,2112,1864],{"className":2113},[659],[573,2115,2118,2121],{"className":2116,"style":2117},[1487],"top:-2.689em;",[573,2119],{"className":2120,"style":652},[651],[573,2122,2125],{"className":2123,"style":2124},[1509],"height:0.522em;min-width:1.469em;",[1512,2126,2130],{"xmlns":1514,"width":1515,"height":2127,"viewBox":2128,"preserveAspectRatio":2129},"0.522em","0 0 400000 522","xMaxYMin slice",[1520,2131],{"d":2132},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[573,2134,1527],{"className":2135},[1526],[573,2137,2139],{"className":2138},[640],[573,2140,2143],{"className":2141,"style":2142},[644],"height:0.011em;",[573,2144],{},[573,2146],{"className":2147,"style":900},[899],[573,2149],{"className":2150,"style":900},[899],[573,2152,2154,2157,2186,2189,2192],{"className":2153},[615],[573,2155],{"className":2156,"style":1911},[619],[573,2158,2160,2163],{"className":2159},[624],[573,2161,1066],{"className":2162,"style":1081},[624,628],[573,2164,2166],{"className":2165},[632],[573,2167,2169],{"className":2168},[636],[573,2170,2172],{"className":2171},[640],[573,2173,2175],{"className":2174,"style":1930},[644],[573,2176,2177,2180],{"style":1933},[573,2178],{"className":2179,"style":652},[651],[573,2181,2183],{"className":2182},[656,657,658,659],[573,2184,682],{"className":2185},[624,659],[573,2187],{"className":2188,"style":1946},[899],[573,2190,1773],{"className":2191},[1950],[573,2193],{"className":2194,"style":1946},[899],[573,2196,2198,2202,2205,2208,2211,2214],{"className":2197},[615],[573,2199],{"className":2200,"style":2201},[619],"height:0.7278em;vertical-align:-0.0833em;",[573,2203,1827],{"className":2204},[624],[573,2206,1066],{"className":2207,"style":1081},[624,628],[573,2209],{"className":2210,"style":1946},[899],[573,2212,1836],{"className":2213},[1950],[573,2215],{"className":2216,"style":1946},[899],[573,2218,2220,2223,2226,2229,2232],{"className":2219},[615],[573,2221],{"className":2222,"style":1406},[619],[573,2224,1839],{"className":2225},[624],[573,2227],{"className":2228,"style":900},[899],[573,2230,837],{"className":2231},[904],[573,2233],{"className":2234,"style":900},[899],[573,2236,2238,2241],{"className":2237},[615],[573,2239],{"className":2240,"style":1406},[619],[573,2242,1374],{"className":2243},[624],[564,2245,2246,2247,2275,2276,2374,2375,2468],{},"Lösungen für ",[573,2248,2250,2263],{"className":2249},[576],[573,2251,2253],{"className":2252},[580],[582,2254,2255],{"xmlns":584},[586,2256,2257,2261],{},[589,2258,2259],{},[595,2260,1066],{},[603,2262,1066],{"encoding":605},[573,2264,2266],{"className":2265,"ariaHidden":611},[610],[573,2267,2269,2272],{"className":2268},[615],[573,2270],{"className":2271,"style":811},[619],[573,2273,1066],{"className":2274,"style":1081},[624,628],": ",[573,2277,2279,2303],{"className":2278},[576],[573,2280,2282],{"className":2281},[580],[582,2283,2284],{"xmlns":584},[586,2285,2286,2300],{},[589,2287,2288,2296,2298],{},[2289,2290,2291,2293],"msub",{},[595,2292,1066],{},[599,2294,2295],{},"1",[835,2297,837],{},[599,2299,601],{},[603,2301,2302],{"encoding":605},"z_1 = 4",[573,2304,2306,2365],{"className":2305,"ariaHidden":611},[610],[573,2307,2309,2313,2356,2359,2362],{"className":2308},[615],[573,2310],{"className":2311,"style":2312},[619],"height:0.5806em;vertical-align:-0.15em;",[573,2314,2316,2319],{"className":2315},[624],[573,2317,1066],{"className":2318,"style":1081},[624,628],[573,2320,2322],{"className":2321},[632],[573,2323,2325,2347],{"className":2324},[636,1476],[573,2326,2328,2344],{"className":2327},[640],[573,2329,2332],{"className":2330,"style":2331},[644],"height:0.3011em;",[573,2333,2335,2338],{"style":2334},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[573,2336],{"className":2337,"style":652},[651],[573,2339,2341],{"className":2340},[656,657,658,659],[573,2342,2295],{"className":2343},[624,659],[573,2345,1527],{"className":2346},[1526],[573,2348,2350],{"className":2349},[640],[573,2351,2354],{"className":2352,"style":2353},[644],"height:0.15em;",[573,2355],{},[573,2357],{"className":2358,"style":900},[899],[573,2360,837],{"className":2361},[904],[573,2363],{"className":2364,"style":900},[899],[573,2366,2368,2371],{"className":2367},[615],[573,2369],{"className":2370,"style":1406},[619],[573,2372,601],{"className":2373},[624]," und ",[573,2376,2378,2401],{"className":2377},[576],[573,2379,2381],{"className":2380},[580],[582,2382,2383],{"xmlns":584},[586,2384,2385,2398],{},[589,2386,2387,2393,2395],{},[2289,2388,2389,2391],{},[595,2390,1066],{},[599,2392,682],{},[835,2394,837],{},[599,2396,2397],{},"9",[603,2399,2400],{"encoding":605},"z_2 = 9",[573,2402,2404,2459],{"className":2403,"ariaHidden":611},[610],[573,2405,2407,2410,2450,2453,2456],{"className":2406},[615],[573,2408],{"className":2409,"style":2312},[619],[573,2411,2413,2416],{"className":2412},[624],[573,2414,1066],{"className":2415,"style":1081},[624,628],[573,2417,2419],{"className":2418},[632],[573,2420,2422,2442],{"className":2421},[636,1476],[573,2423,2425,2439],{"className":2424},[640],[573,2426,2428],{"className":2427,"style":2331},[644],[573,2429,2430,2433],{"style":2334},[573,2431],{"className":2432,"style":652},[651],[573,2434,2436],{"className":2435},[656,657,658,659],[573,2437,682],{"className":2438},[624,659],[573,2440,1527],{"className":2441},[1526],[573,2443,2445],{"className":2444},[640],[573,2446,2448],{"className":2447,"style":2353},[644],[573,2449],{},[573,2451],{"className":2452,"style":900},[899],[573,2454,837],{"className":2455},[904],[573,2457],{"className":2458,"style":900},[899],[573,2460,2462,2465],{"className":2461},[615],[573,2463],{"className":2464,"style":1406},[619],[573,2466,2397],{"className":2467},[624],". Resubstitution:",[573,2470,2472],{"className":2471},[1803],[573,2473,2475,2531],{"className":2474},[576],[573,2476,2478],{"className":2477},[580],[582,2479,2480],{"xmlns":584,"display":1812},[586,2481,2482,2528],{},[589,2483,2484,2490,2492,2494,2497,2499,2501,2503,2505,2508,2514,2516,2518,2520,2522,2524,2526],{},[592,2485,2486,2488],{},[595,2487,597],{},[599,2489,682],{},[835,2491,837],{},[599,2493,601],{},[835,2495,2496],{},"⇒",[595,2498,597],{},[835,2500,837],{},[835,2502,1429],{},[599,2504,682],{},[899,2506],{"width":2507},"2em",[592,2509,2510,2512],{},[595,2511,597],{},[599,2513,682],{},[835,2515,837],{},[599,2517,2397],{},[835,2519,2496],{},[595,2521,597],{},[835,2523,837],{},[835,2525,1429],{},[599,2527,743],{},[603,2529,2530],{"encoding":605},"x^2 = 4 \\Rightarrow x = \\pm 2 \\qquad x^2 = 9 \\Rightarrow x = \\pm 3",[573,2532,2534,2578,2596,2614,2668,2686,2704],{"className":2533,"ariaHidden":611},[610],[573,2535,2537,2540,2569,2572,2575],{"className":2536},[615],[573,2538],{"className":2539,"style":1930},[619],[573,2541,2543,2546],{"className":2542},[624],[573,2544,597],{"className":2545},[624,628],[573,2547,2549],{"className":2548},[632],[573,2550,2552],{"className":2551},[636],[573,2553,2555],{"className":2554},[640],[573,2556,2558],{"className":2557,"style":1930},[644],[573,2559,2560,2563],{"style":1933},[573,2561],{"className":2562,"style":652},[651],[573,2564,2566],{"className":2565},[656,657,658,659],[573,2567,682],{"className":2568},[624,659],[573,2570],{"className":2571,"style":900},[899],[573,2573,837],{"className":2574},[904],[573,2576],{"className":2577,"style":900},[899],[573,2579,2581,2584,2587,2590,2593],{"className":2580},[615],[573,2582],{"className":2583,"style":1406},[619],[573,2585,601],{"className":2586},[624],[573,2588],{"className":2589,"style":900},[899],[573,2591,2496],{"className":2592},[904],[573,2594],{"className":2595,"style":900},[899],[573,2597,2599,2602,2605,2608,2611],{"className":2598},[615],[573,2600],{"className":2601,"style":811},[619],[573,2603,597],{"className":2604},[624,628],[573,2606],{"className":2607,"style":900},[899],[573,2609,837],{"className":2610},[904],[573,2612],{"className":2613,"style":900},[899],[573,2615,2617,2620,2623,2626,2630,2659,2662,2665],{"className":2616},[615],[573,2618],{"className":2619,"style":1911},[619],[573,2621,1429],{"className":2622},[624],[573,2624,682],{"className":2625},[624],[573,2627],{"className":2628,"style":2629},[899],"margin-right:2em;",[573,2631,2633,2636],{"className":2632},[624],[573,2634,597],{"className":2635},[624,628],[573,2637,2639],{"className":2638},[632],[573,2640,2642],{"className":2641},[636],[573,2643,2645],{"className":2644},[640],[573,2646,2648],{"className":2647,"style":1930},[644],[573,2649,2650,2653],{"style":1933},[573,2651],{"className":2652,"style":652},[651],[573,2654,2656],{"className":2655},[656,657,658,659],[573,2657,682],{"className":2658},[624,659],[573,2660],{"className":2661,"style":900},[899],[573,2663,837],{"className":2664},[904],[573,2666],{"className":2667,"style":900},[899],[573,2669,2671,2674,2677,2680,2683],{"className":2670},[615],[573,2672],{"className":2673,"style":1406},[619],[573,2675,2397],{"className":2676},[624],[573,2678],{"className":2679,"style":900},[899],[573,2681,2496],{"className":2682},[904],[573,2684],{"className":2685,"style":900},[899],[573,2687,2689,2692,2695,2698,2701],{"className":2688},[615],[573,2690],{"className":2691,"style":811},[619],[573,2693,597],{"className":2694},[624,628],[573,2696],{"className":2697,"style":900},[899],[573,2699,837],{"className":2700},[904],[573,2702],{"className":2703,"style":900},[899],[573,2705,2707,2710,2713],{"className":2706},[615],[573,2708],{"className":2709,"style":2201},[619],[573,2711,1429],{"className":2712},[624],[573,2714,743],{"className":2715},[624],[564,2717,2718,2719,1200],{},"Vier Lösungen: ",[573,2720,2722,2771],{"className":2721},[576],[573,2723,2725],{"className":2724},[580],[582,2726,2727],{"xmlns":584},[586,2728,2729,2768],{},[589,2730,2731,2735,2737,2740,2742,2744,2747,2749,2751,2753,2755,2757,2759,2761,2763,2765],{},[595,2732,2734],{"mathvariant":2733},"double-struck","L",[835,2736,837],{},[835,2738,2739],{"stretchy":840},"{",[835,2741,1773],{},[599,2743,743],{},[835,2745,2746],{"separator":611},";",[1845,2748,1864],{},[835,2750,1773],{},[599,2752,682],{},[835,2754,2746],{"separator":611},[1845,2756,1864],{},[599,2758,682],{},[835,2760,2746],{"separator":611},[1845,2762,1864],{},[599,2764,743],{},[835,2766,2767],{"stretchy":840},"}",[603,2769,2770],{"encoding":605},"\\mathbb{L} = \\{-3;\\ -2;\\ 2;\\ 3\\}",[573,2772,2774,2794],{"className":2773,"ariaHidden":611},[610],[573,2775,2777,2781,2785,2788,2791],{"className":2776},[615],[573,2778],{"className":2779,"style":2780},[619],"height:0.6889em;",[573,2782,2734],{"className":2783},[624,2784],"mathbb",[573,2786],{"className":2787,"style":900},[899],[573,2789,837],{"className":2790},[904],[573,2792],{"className":2793,"style":900},[899],[573,2795,2797,2801,2804,2807,2810,2814,2817,2821,2824,2827,2830,2833,2836,2839,2842,2845,2848,2851],{"className":2796},[615],[573,2798],{"className":2799,"style":2800},[619],"height:1em;vertical-align:-0.25em;",[573,2802,2739],{"className":2803},[918],[573,2805,1773],{"className":2806},[624],[573,2808,743],{"className":2809},[624],[573,2811,2746],{"className":2812},[2813],"mpunct",[573,2815,1864],{"className":2816},[899],[573,2818],{"className":2819,"style":2820},[899],"margin-right:0.1667em;",[573,2822,1773],{"className":2823},[624],[573,2825,682],{"className":2826},[624],[573,2828,2746],{"className":2829},[2813],[573,2831,1864],{"className":2832},[899],[573,2834],{"className":2835,"style":2820},[899],[573,2837,682],{"className":2838},[624],[573,2840,2746],{"className":2841},[2813],[573,2843,1864],{"className":2844},[899],[573,2846],{"className":2847,"style":2820},[899],[573,2849,743],{"className":2850},[624],[573,2852,2767],{"className":2853},[951],[564,2855,2856,2857,2885],{},"Mit einer negativen Lösung für ",[573,2858,2860,2873],{"className":2859},[576],[573,2861,2863],{"className":2862},[580],[582,2864,2865],{"xmlns":584},[586,2866,2867,2871],{},[589,2868,2869],{},[595,2870,1066],{},[603,2872,1066],{"encoding":605},[573,2874,2876],{"className":2875,"ariaHidden":611},[610],[573,2877,2879,2882],{"className":2878},[615],[573,2880],{"className":2881,"style":811},[619],[573,2883,1066],{"className":2884,"style":1081},[624,628],":",[573,2887,2889],{"className":2888},[1803],[573,2890,2892,2974],{"className":2891},[576],[573,2893,2895],{"className":2894},[580],[582,2896,2897],{"xmlns":584,"display":1812},[586,2898,2899,2971],{},[589,2900,2901,2907,2909,2911,2917,2919,2921,2923,2925,2927,2949,2951,2957,2959,2961,2963,2965,2967,2969],{},[592,2902,2903,2905],{},[595,2904,597],{},[599,2906,601],{},[835,2908,1836],{},[599,2910,743],{},[592,2912,2913,2915],{},[595,2914,597],{},[599,2916,682],{},[835,2918,1773],{},[599,2920,601],{},[835,2922,837],{},[599,2924,1374],{},[1845,2926,1847],{},[1849,2928,2929,2931],{},[835,2930,1854],{"stretchy":611,"minsize":1853},[1856,2932,2933],{"width":1858,"lspace":1859},[589,2934,2935,2937,2939,2941,2947],{},[1845,2936,1864],{},[595,2938,1066],{},[835,2940,837],{},[592,2942,2943,2945],{},[595,2944,597],{},[599,2946,682],{},[1845,2948,1864],{},[1845,2950,1847],{},[592,2952,2953,2955],{},[595,2954,1066],{},[599,2956,682],{},[835,2958,1836],{},[599,2960,743],{},[595,2962,1066],{},[835,2964,1773],{},[599,2966,601],{},[835,2968,837],{},[599,2970,1374],{},[603,2972,2973],{"encoding":605},"x^4 + 3x^2 - 4 = 0 \\;\\xrightarrow{\\ z = x^2\\ }\\; z^2 + 3z - 4 = 0",[573,2975,2977,3021,3068,3086,3201,3245,3266,3284],{"className":2976,"ariaHidden":611},[610],[573,2978,2980,2983,3012,3015,3018],{"className":2979},[615],[573,2981],{"className":2982,"style":1911},[619],[573,2984,2986,2989],{"className":2985},[624],[573,2987,597],{"className":2988},[624,628],[573,2990,2992],{"className":2991},[632],[573,2993,2995],{"className":2994},[636],[573,2996,2998],{"className":2997},[640],[573,2999,3001],{"className":3000,"style":1930},[644],[573,3002,3003,3006],{"style":1933},[573,3004],{"className":3005,"style":652},[651],[573,3007,3009],{"className":3008},[656,657,658,659],[573,3010,601],{"className":3011},[624,659],[573,3013],{"className":3014,"style":1946},[899],[573,3016,1836],{"className":3017},[1950],[573,3019],{"className":3020,"style":1946},[899],[573,3022,3024,3027,3030,3059,3062,3065],{"className":3023},[615],[573,3025],{"className":3026,"style":1911},[619],[573,3028,743],{"className":3029},[624],[573,3031,3033,3036],{"className":3032},[624],[573,3034,597],{"className":3035},[624,628],[573,3037,3039],{"className":3038},[632],[573,3040,3042],{"className":3041},[636],[573,3043,3045],{"className":3044},[640],[573,3046,3048],{"className":3047,"style":1930},[644],[573,3049,3050,3053],{"style":1933},[573,3051],{"className":3052,"style":652},[651],[573,3054,3056],{"className":3055},[656,657,658,659],[573,3057,682],{"className":3058},[624,659],[573,3060],{"className":3061,"style":1946},[899],[573,3063,1773],{"className":3064},[1950],[573,3066],{"className":3067,"style":1946},[899],[573,3069,3071,3074,3077,3080,3083],{"className":3070},[615],[573,3072],{"className":3073,"style":1406},[619],[573,3075,601],{"className":3076},[624],[573,3078],{"className":3079,"style":900},[899],[573,3081,837],{"className":3082},[904],[573,3084],{"className":3085,"style":900},[899],[573,3087,3089,3092,3095,3098,3101,3195,3198],{"className":3088},[615],[573,3090],{"className":3091,"style":2025},[619],[573,3093,1374],{"className":3094},[624],[573,3096],{"className":3097,"style":900},[899],[573,3099],{"className":3100,"style":900},[899],[573,3102,3104],{"className":3103},[904,2038],[573,3105,3107,3187],{"className":3106},[636,1476],[573,3108,3110,3184],{"className":3109},[640],[573,3111,3113,3171],{"className":3112,"style":2048},[644],[573,3114,3115,3118],{"style":2051},[573,3116],{"className":3117,"style":652},[651],[573,3119,3121],{"className":3120},[656,657,658,659,2058],[573,3122,3124,3130,3133,3136,3165],{"className":3123},[624,659],[573,3125,3127],{"className":3126},[899,659],[573,3128,1864],{"className":3129},[659],[573,3131,1066],{"className":3132,"style":1081},[624,628,659],[573,3134,837],{"className":3135},[904,659],[573,3137,3139,3142],{"className":3138},[624,659],[573,3140,597],{"className":3141},[624,628,659],[573,3143,3145],{"className":3144},[632],[573,3146,3148],{"className":3147},[636],[573,3149,3151],{"className":3150},[640],[573,3152,3154],{"className":3153,"style":2092},[644],[573,3155,3156,3159],{"style":2095},[573,3157],{"className":3158,"style":2099},[651],[573,3160,3162],{"className":3161},[656,2103,2104,659],[573,3163,682],{"className":3164},[624,659],[573,3166,3168],{"className":3167},[899,659],[573,3169,1864],{"className":3170},[659],[573,3172,3174,3177],{"className":3173,"style":2117},[1487],[573,3175],{"className":3176,"style":652},[651],[573,3178,3180],{"className":3179,"style":2124},[1509],[1512,3181,3182],{"xmlns":1514,"width":1515,"height":2127,"viewBox":2128,"preserveAspectRatio":2129},[1520,3183],{"d":2132},[573,3185,1527],{"className":3186},[1526],[573,3188,3190],{"className":3189},[640],[573,3191,3193],{"className":3192,"style":2142},[644],[573,3194],{},[573,3196],{"className":3197,"style":900},[899],[573,3199],{"className":3200,"style":900},[899],[573,3202,3204,3207,3236,3239,3242],{"className":3203},[615],[573,3205],{"className":3206,"style":1911},[619],[573,3208,3210,3213],{"className":3209},[624],[573,3211,1066],{"className":3212,"style":1081},[624,628],[573,3214,3216],{"className":3215},[632],[573,3217,3219],{"className":3218},[636],[573,3220,3222],{"className":3221},[640],[573,3223,3225],{"className":3224,"style":1930},[644],[573,3226,3227,3230],{"style":1933},[573,3228],{"className":3229,"style":652},[651],[573,3231,3233],{"className":3232},[656,657,658,659],[573,3234,682],{"className":3235},[624,659],[573,3237],{"className":3238,"style":1946},[899],[573,3240,1836],{"className":3241},[1950],[573,3243],{"className":3244,"style":1946},[899],[573,3246,3248,3251,3254,3257,3260,3263],{"className":3247},[615],[573,3249],{"className":3250,"style":2201},[619],[573,3252,743],{"className":3253},[624],[573,3255,1066],{"className":3256,"style":1081},[624,628],[573,3258],{"className":3259,"style":1946},[899],[573,3261,1773],{"className":3262},[1950],[573,3264],{"className":3265,"style":1946},[899],[573,3267,3269,3272,3275,3278,3281],{"className":3268},[615],[573,3270],{"className":3271,"style":1406},[619],[573,3273,601],{"className":3274},[624],[573,3276],{"className":3277,"style":900},[899],[573,3279,837],{"className":3280},[904],[573,3282],{"className":3283,"style":900},[899],[573,3285,3287,3290],{"className":3286},[615],[573,3288],{"className":3289,"style":1406},[619],[573,3291,1374],{"className":3292},[624],[564,3294,3295,3296,2374,3388,3485,3486,3567,3568,3624,3625,3711,3712,1200],{},"Lösungen ",[573,3297,3299,3321],{"className":3298},[576],[573,3300,3302],{"className":3301},[580],[582,3303,3304],{"xmlns":584},[586,3305,3306,3318],{},[589,3307,3308,3314,3316],{},[2289,3309,3310,3312],{},[595,3311,1066],{},[599,3313,2295],{},[835,3315,837],{},[599,3317,2295],{},[603,3319,3320],{"encoding":605},"z_1 = 1",[573,3322,3324,3379],{"className":3323,"ariaHidden":611},[610],[573,3325,3327,3330,3370,3373,3376],{"className":3326},[615],[573,3328],{"className":3329,"style":2312},[619],[573,3331,3333,3336],{"className":3332},[624],[573,3334,1066],{"className":3335,"style":1081},[624,628],[573,3337,3339],{"className":3338},[632],[573,3340,3342,3362],{"className":3341},[636,1476],[573,3343,3345,3359],{"className":3344},[640],[573,3346,3348],{"className":3347,"style":2331},[644],[573,3349,3350,3353],{"style":2334},[573,3351],{"className":3352,"style":652},[651],[573,3354,3356],{"className":3355},[656,657,658,659],[573,3357,2295],{"className":3358},[624,659],[573,3360,1527],{"className":3361},[1526],[573,3363,3365],{"className":3364},[640],[573,3366,3368],{"className":3367,"style":2353},[644],[573,3369],{},[573,3371],{"className":3372,"style":900},[899],[573,3374,837],{"className":3375},[904],[573,3377],{"className":3378,"style":900},[899],[573,3380,3382,3385],{"className":3381},[615],[573,3383],{"className":3384,"style":1406},[619],[573,3386,2295],{"className":3387},[624],[573,3389,3391,3415],{"className":3390},[576],[573,3392,3394],{"className":3393},[580],[582,3395,3396],{"xmlns":584},[586,3397,3398,3412],{},[589,3399,3400,3406,3408,3410],{},[2289,3401,3402,3404],{},[595,3403,1066],{},[599,3405,682],{},[835,3407,837],{},[835,3409,1773],{},[599,3411,601],{},[603,3413,3414],{"encoding":605},"z_2 = -4",[573,3416,3418,3473],{"className":3417,"ariaHidden":611},[610],[573,3419,3421,3424,3464,3467,3470],{"className":3420},[615],[573,3422],{"className":3423,"style":2312},[619],[573,3425,3427,3430],{"className":3426},[624],[573,3428,1066],{"className":3429,"style":1081},[624,628],[573,3431,3433],{"className":3432},[632],[573,3434,3436,3456],{"className":3435},[636,1476],[573,3437,3439,3453],{"className":3438},[640],[573,3440,3442],{"className":3441,"style":2331},[644],[573,3443,3444,3447],{"style":2334},[573,3445],{"className":3446,"style":652},[651],[573,3448,3450],{"className":3449},[656,657,658,659],[573,3451,682],{"className":3452},[624,659],[573,3454,1527],{"className":3455},[1526],[573,3457,3459],{"className":3458},[640],[573,3460,3462],{"className":3461,"style":2353},[644],[573,3463],{},[573,3465],{"className":3466,"style":900},[899],[573,3468,837],{"className":3469},[904],[573,3471],{"className":3472,"style":900},[899],[573,3474,3476,3479,3482],{"className":3475},[615],[573,3477],{"className":3478,"style":2201},[619],[573,3480,1773],{"className":3481},[624],[573,3483,601],{"className":3484},[624],". Aus ",[573,3487,3489,3511],{"className":3488},[576],[573,3490,3492],{"className":3491},[580],[582,3493,3494],{"xmlns":584},[586,3495,3496,3508],{},[589,3497,3498,3504,3506],{},[592,3499,3500,3502],{},[595,3501,597],{},[599,3503,682],{},[835,3505,837],{},[599,3507,2295],{},[603,3509,3510],{"encoding":605},"x^2 = 1",[573,3512,3514,3558],{"className":3513,"ariaHidden":611},[610],[573,3515,3517,3520,3549,3552,3555],{"className":3516},[615],[573,3518],{"className":3519,"style":620},[619],[573,3521,3523,3526],{"className":3522},[624],[573,3524,597],{"className":3525},[624,628],[573,3527,3529],{"className":3528},[632],[573,3530,3532],{"className":3531},[636],[573,3533,3535],{"className":3534},[640],[573,3536,3538],{"className":3537,"style":620},[644],[573,3539,3540,3543],{"style":647},[573,3541],{"className":3542,"style":652},[651],[573,3544,3546],{"className":3545},[656,657,658,659],[573,3547,682],{"className":3548},[624,659],[573,3550],{"className":3551,"style":900},[899],[573,3553,837],{"className":3554},[904],[573,3556],{"className":3557,"style":900},[899],[573,3559,3561,3564],{"className":3560},[615],[573,3562],{"className":3563,"style":1406},[619],[573,3565,2295],{"className":3566},[624]," folgt ",[573,3569,3571,3591],{"className":3570},[576],[573,3572,3574],{"className":3573},[580],[582,3575,3576],{"xmlns":584},[586,3577,3578,3588],{},[589,3579,3580,3582,3584,3586],{},[595,3581,597],{},[835,3583,837],{},[835,3585,1429],{},[599,3587,2295],{},[603,3589,3590],{"encoding":605},"x = \\pm 1",[573,3592,3594,3612],{"className":3593,"ariaHidden":611},[610],[573,3595,3597,3600,3603,3606,3609],{"className":3596},[615],[573,3598],{"className":3599,"style":811},[619],[573,3601,597],{"className":3602},[624,628],[573,3604],{"className":3605,"style":900},[899],[573,3607,837],{"className":3608},[904],[573,3610],{"className":3611,"style":900},[899],[573,3613,3615,3618,3621],{"className":3614},[615],[573,3616],{"className":3617,"style":2201},[619],[573,3619,1429],{"className":3620},[624],[573,3622,2295],{"className":3623},[624],". Die Gleichung ",[573,3626,3628,3652],{"className":3627},[576],[573,3629,3631],{"className":3630},[580],[582,3632,3633],{"xmlns":584},[586,3634,3635,3649],{},[589,3636,3637,3643,3645,3647],{},[592,3638,3639,3641],{},[595,3640,597],{},[599,3642,682],{},[835,3644,837],{},[835,3646,1773],{},[599,3648,601],{},[603,3650,3651],{"encoding":605},"x^2 = -4",[573,3653,3655,3699],{"className":3654,"ariaHidden":611},[610],[573,3656,3658,3661,3690,3693,3696],{"className":3657},[615],[573,3659],{"className":3660,"style":620},[619],[573,3662,3664,3667],{"className":3663},[624],[573,3665,597],{"className":3666},[624,628],[573,3668,3670],{"className":3669},[632],[573,3671,3673],{"className":3672},[636],[573,3674,3676],{"className":3675},[640],[573,3677,3679],{"className":3678,"style":620},[644],[573,3680,3681,3684],{"style":647},[573,3682],{"className":3683,"style":652},[651],[573,3685,3687],{"className":3686},[656,657,658,659],[573,3688,682],{"className":3689},[624,659],[573,3691],{"className":3692,"style":900},[899],[573,3694,837],{"className":3695},[904],[573,3697],{"className":3698,"style":900},[899],[573,3700,3702,3705,3708],{"className":3701},[615],[573,3703],{"className":3704,"style":2201},[619],[573,3706,1773],{"className":3707},[624],[573,3709,601],{"className":3710},[624]," hat keine reelle Lösung. Also ",[573,3713,3715,3745],{"className":3714},[576],[573,3716,3718],{"className":3717},[580],[582,3719,3720],{"xmlns":584},[586,3721,3722,3742],{},[589,3723,3724,3726,3728,3730,3732,3734,3736,3738,3740],{},[595,3725,2734],{"mathvariant":2733},[835,3727,837],{},[835,3729,2739],{"stretchy":840},[835,3731,1773],{},[599,3733,2295],{},[835,3735,2746],{"separator":611},[1845,3737,1864],{},[599,3739,2295],{},[835,3741,2767],{"stretchy":840},[603,3743,3744],{"encoding":605},"\\mathbb{L} = \\{-1;\\ 1\\}",[573,3746,3748,3766],{"className":3747,"ariaHidden":611},[610],[573,3749,3751,3754,3757,3760,3763],{"className":3750},[615],[573,3752],{"className":3753,"style":2780},[619],[573,3755,2734],{"className":3756},[624,2784],[573,3758],{"className":3759,"style":900},[899],[573,3761,837],{"className":3762},[904],[573,3764],{"className":3765,"style":900},[899],[573,3767,3769,3772,3775,3778,3781,3784,3787,3790,3793],{"className":3768},[615],[573,3770],{"className":3771,"style":2800},[619],[573,3773,2739],{"className":3774},[918],[573,3776,1773],{"className":3777},[624],[573,3779,2295],{"className":3780},[624],[573,3782,2746],{"className":3783},[2813],[573,3785,1864],{"className":3786},[899],[573,3788],{"className":3789,"style":2820},[899],[573,3791,2295],{"className":3792},[624],[573,3794,2767],{"className":3795},[951],[564,3797,3798],{},"Fehlt die Zahl, klammert man besser aus, statt zu substituieren:",[573,3800,3802],{"className":3801},[1803],[573,3803,3805,3874],{"className":3804},[576],[573,3806,3808],{"className":3807},[580],[582,3809,3810],{"xmlns":584,"display":1812},[586,3811,3812,3871],{},[589,3813,3814,3816,3822,3824,3827,3833,3835,3837,3839,3841,3843,3845,3851,3867,3869],{},[599,3815,682],{},[592,3817,3818,3820],{},[595,3819,597],{},[599,3821,601],{},[835,3823,1773],{},[599,3825,3826],{},"8",[592,3828,3829,3831],{},[595,3830,597],{},[599,3832,682],{},[835,3834,837],{},[599,3836,1374],{},[1845,3838,1847],{},[835,3840,2496],{},[1845,3842,1847],{},[599,3844,682],{},[592,3846,3847,3849],{},[595,3848,597],{},[599,3850,682],{},[589,3852,3853,3855,3861,3863,3865],{},[835,3854,841],{"fence":611},[592,3856,3857,3859],{},[595,3858,597],{},[599,3860,682],{},[835,3862,1773],{},[599,3864,601],{},[835,3866,852],{"fence":611},[835,3868,837],{},[599,3870,1374],{},[603,3872,3873],{"encoding":605},"2x^4 - 8x^2 = 0 \\;\\Rightarrow\\; 2x^2\\left(x^2 - 4\\right) = 0",[573,3875,3877,3924,3971,3995,4106],{"className":3876,"ariaHidden":611},[610],[573,3878,3880,3883,3886,3915,3918,3921],{"className":3879},[615],[573,3881],{"className":3882,"style":1911},[619],[573,3884,682],{"className":3885},[624],[573,3887,3889,3892],{"className":3888},[624],[573,3890,597],{"className":3891},[624,628],[573,3893,3895],{"className":3894},[632],[573,3896,3898],{"className":3897},[636],[573,3899,3901],{"className":3900},[640],[573,3902,3904],{"className":3903,"style":1930},[644],[573,3905,3906,3909],{"style":1933},[573,3907],{"className":3908,"style":652},[651],[573,3910,3912],{"className":3911},[656,657,658,659],[573,3913,601],{"className":3914},[624,659],[573,3916],{"className":3917,"style":1946},[899],[573,3919,1773],{"className":3920},[1950],[573,3922],{"className":3923,"style":1946},[899],[573,3925,3927,3930,3933,3962,3965,3968],{"className":3926},[615],[573,3928],{"className":3929,"style":1930},[619],[573,3931,3826],{"className":3932},[624],[573,3934,3936,3939],{"className":3935},[624],[573,3937,597],{"className":3938},[624,628],[573,3940,3942],{"className":3941},[632],[573,3943,3945],{"className":3944},[636],[573,3946,3948],{"className":3947},[640],[573,3949,3951],{"className":3950,"style":1930},[644],[573,3952,3953,3956],{"style":1933},[573,3954],{"className":3955,"style":652},[651],[573,3957,3959],{"className":3958},[656,657,658,659],[573,3960,682],{"className":3961},[624,659],[573,3963],{"className":3964,"style":900},[899],[573,3966,837],{"className":3967},[904],[573,3969],{"className":3970,"style":900},[899],[573,3972,3974,3977,3980,3983,3986,3989,3992],{"className":3973},[615],[573,3975],{"className":3976,"style":1406},[619],[573,3978,1374],{"className":3979},[624],[573,3981],{"className":3982,"style":900},[899],[573,3984],{"className":3985,"style":900},[899],[573,3987,2496],{"className":3988},[904],[573,3990],{"className":3991,"style":900},[899],[573,3993],{"className":3994,"style":900},[899],[573,3996,3998,4002,4005,4034,4037,4097,4100,4103],{"className":3997},[615],[573,3999],{"className":4000,"style":4001},[619],"height:1.2141em;vertical-align:-0.35em;",[573,4003,682],{"className":4004},[624],[573,4006,4008,4011],{"className":4007},[624],[573,4009,597],{"className":4010},[624,628],[573,4012,4014],{"className":4013},[632],[573,4015,4017],{"className":4016},[636],[573,4018,4020],{"className":4019},[640],[573,4021,4023],{"className":4022,"style":1930},[644],[573,4024,4025,4028],{"style":1933},[573,4026],{"className":4027,"style":652},[651],[573,4029,4031],{"className":4030},[656,657,658,659],[573,4032,682],{"className":4033},[624,659],[573,4035],{"className":4036,"style":2820},[899],[573,4038,4041,4050,4079,4082,4085,4088,4091],{"className":4039},[4040],"minner",[573,4042,4046],{"className":4043,"style":4045},[918,4044],"delimcenter","top:0em;",[573,4047,841],{"className":4048},[4049,2104],"delimsizing",[573,4051,4053,4056],{"className":4052},[624],[573,4054,597],{"className":4055},[624,628],[573,4057,4059],{"className":4058},[632],[573,4060,4062],{"className":4061},[636],[573,4063,4065],{"className":4064},[640],[573,4066,4068],{"className":4067,"style":1930},[644],[573,4069,4070,4073],{"style":1933},[573,4071],{"className":4072,"style":652},[651],[573,4074,4076],{"className":4075},[656,657,658,659],[573,4077,682],{"className":4078},[624,659],[573,4080],{"className":4081,"style":1946},[899],[573,4083,1773],{"className":4084},[1950],[573,4086],{"className":4087,"style":1946},[899],[573,4089,601],{"className":4090},[624],[573,4092,4094],{"className":4093,"style":4045},[951,4044],[573,4095,852],{"className":4096},[4049,2104],[573,4098],{"className":4099,"style":900},[899],[573,4101,837],{"className":4102},[904],[573,4104],{"className":4105,"style":900},[899],[573,4107,4109,4112],{"className":4108},[615],[573,4110],{"className":4111,"style":1406},[619],[573,4113,1374],{"className":4114},[624],[564,4116,4117,4118,4168,4169,1200],{},"Nach dem Satz vom Nullprodukt gilt ",[573,4119,4121,4138],{"className":4120},[576],[573,4122,4124],{"className":4123},[580],[582,4125,4126],{"xmlns":584},[586,4127,4128,4136],{},[589,4129,4130,4132,4134],{},[595,4131,597],{},[835,4133,837],{},[599,4135,1374],{},[603,4137,1612],{"encoding":605},[573,4139,4141,4159],{"className":4140,"ariaHidden":611},[610],[573,4142,4144,4147,4150,4153,4156],{"className":4143},[615],[573,4145],{"className":4146,"style":811},[619],[573,4148,597],{"className":4149},[624,628],[573,4151],{"className":4152,"style":900},[899],[573,4154,837],{"className":4155},[904],[573,4157],{"className":4158,"style":900},[899],[573,4160,4162,4165],{"className":4161},[615],[573,4163],{"className":4164,"style":1406},[619],[573,4166,1374],{"className":4167},[624]," oder ",[573,4170,4172,4192],{"className":4171},[576],[573,4173,4175],{"className":4174},[580],[582,4176,4177],{"xmlns":584},[586,4178,4179,4189],{},[589,4180,4181,4183,4185,4187],{},[595,4182,597],{},[835,4184,837],{},[835,4186,1429],{},[599,4188,682],{},[603,4190,4191],{"encoding":605},"x = \\pm 2",[573,4193,4195,4213],{"className":4194,"ariaHidden":611},[610],[573,4196,4198,4201,4204,4207,4210],{"className":4197},[615],[573,4199],{"className":4200,"style":811},[619],[573,4202,597],{"className":4203},[624,628],[573,4205],{"className":4206,"style":900},[899],[573,4208,837],{"className":4209},[904],[573,4211],{"className":4212,"style":900},[899],[573,4214,4216,4219,4222],{"className":4215},[615],[573,4217],{"className":4218,"style":2201},[619],[573,4220,1429],{"className":4221},[624],[573,4223,682],{"className":4224},[624],[559,4226,4228],{"id":4227},"typische-fehler","Typische Fehler",[1351,4230,4231,4474,4668,4786],{},[987,4232,4233,4234,663,4325,4416,4417,4445,4446,1200],{},"Die Resubstitution vergessen und ",[573,4235,4237,4258],{"className":4236},[576],[573,4238,4240],{"className":4239},[580],[582,4241,4242],{"xmlns":584},[586,4243,4244,4256],{},[589,4245,4246,4252,4254],{},[2289,4247,4248,4250],{},[595,4249,1066],{},[599,4251,2295],{},[835,4253,837],{},[599,4255,601],{},[603,4257,2302],{"encoding":605},[573,4259,4261,4316],{"className":4260,"ariaHidden":611},[610],[573,4262,4264,4267,4307,4310,4313],{"className":4263},[615],[573,4265],{"className":4266,"style":2312},[619],[573,4268,4270,4273],{"className":4269},[624],[573,4271,1066],{"className":4272,"style":1081},[624,628],[573,4274,4276],{"className":4275},[632],[573,4277,4279,4299],{"className":4278},[636,1476],[573,4280,4282,4296],{"className":4281},[640],[573,4283,4285],{"className":4284,"style":2331},[644],[573,4286,4287,4290],{"style":2334},[573,4288],{"className":4289,"style":652},[651],[573,4291,4293],{"className":4292},[656,657,658,659],[573,4294,2295],{"className":4295},[624,659],[573,4297,1527],{"className":4298},[1526],[573,4300,4302],{"className":4301},[640],[573,4303,4305],{"className":4304,"style":2353},[644],[573,4306],{},[573,4308],{"className":4309,"style":900},[899],[573,4311,837],{"className":4312},[904],[573,4314],{"className":4315,"style":900},[899],[573,4317,4319,4322],{"className":4318},[615],[573,4320],{"className":4321,"style":1406},[619],[573,4323,601],{"className":4324},[624],[573,4326,4328,4349],{"className":4327},[576],[573,4329,4331],{"className":4330},[580],[582,4332,4333],{"xmlns":584},[586,4334,4335,4347],{},[589,4336,4337,4343,4345],{},[2289,4338,4339,4341],{},[595,4340,1066],{},[599,4342,682],{},[835,4344,837],{},[599,4346,2397],{},[603,4348,2400],{"encoding":605},[573,4350,4352,4407],{"className":4351,"ariaHidden":611},[610],[573,4353,4355,4358,4398,4401,4404],{"className":4354},[615],[573,4356],{"className":4357,"style":2312},[619],[573,4359,4361,4364],{"className":4360},[624],[573,4362,1066],{"className":4363,"style":1081},[624,628],[573,4365,4367],{"className":4366},[632],[573,4368,4370,4390],{"className":4369},[636,1476],[573,4371,4373,4387],{"className":4372},[640],[573,4374,4376],{"className":4375,"style":2331},[644],[573,4377,4378,4381],{"style":2334},[573,4379],{"className":4380,"style":652},[651],[573,4382,4384],{"className":4383},[656,657,658,659],[573,4385,682],{"className":4386},[624,659],[573,4388,1527],{"className":4389},[1526],[573,4391,4393],{"className":4392},[640],[573,4394,4396],{"className":4395,"style":2353},[644],[573,4397],{},[573,4399],{"className":4400,"style":900},[899],[573,4402,837],{"className":4403},[904],[573,4405],{"className":4406,"style":900},[899],[573,4408,4410,4413],{"className":4409},[615],[573,4411],{"className":4412,"style":1406},[619],[573,4414,2397],{"className":4415},[624]," als Lösungen angeben. Gesucht ist ",[573,4418,4420,4433],{"className":4419},[576],[573,4421,4423],{"className":4422},[580],[582,4424,4425],{"xmlns":584},[586,4426,4427,4431],{},[589,4428,4429],{},[595,4430,597],{},[603,4432,597],{"encoding":605},[573,4434,4436],{"className":4435,"ariaHidden":611},[610],[573,4437,4439,4442],{"className":4438},[615],[573,4440],{"className":4441,"style":811},[619],[573,4443,597],{"className":4444},[624,628],", nicht ",[573,4447,4449,4462],{"className":4448},[576],[573,4450,4452],{"className":4451},[580],[582,4453,4454],{"xmlns":584},[586,4455,4456,4460],{},[589,4457,4458],{},[595,4459,1066],{},[603,4461,1066],{"encoding":605},[573,4463,4465],{"className":4464,"ariaHidden":611},[610],[573,4466,4468,4471],{"className":4467},[615],[573,4469],{"className":4470,"style":811},[619],[573,4472,1066],{"className":4473,"style":1081},[624,628],[987,4475,4476,4477,3567,4558,992,4609,992,4612,1200],{},"Nur die positive Wurzel nehmen: Aus ",[573,4478,4480,4502],{"className":4479},[576],[573,4481,4483],{"className":4482},[580],[582,4484,4485],{"xmlns":584},[586,4486,4487,4499],{},[589,4488,4489,4495,4497],{},[592,4490,4491,4493],{},[595,4492,597],{},[599,4494,682],{},[835,4496,837],{},[599,4498,601],{},[603,4500,4501],{"encoding":605},"x^2 = 4",[573,4503,4505,4549],{"className":4504,"ariaHidden":611},[610],[573,4506,4508,4511,4540,4543,4546],{"className":4507},[615],[573,4509],{"className":4510,"style":620},[619],[573,4512,4514,4517],{"className":4513},[624],[573,4515,597],{"className":4516},[624,628],[573,4518,4520],{"className":4519},[632],[573,4521,4523],{"className":4522},[636],[573,4524,4526],{"className":4525},[640],[573,4527,4529],{"className":4528,"style":620},[644],[573,4530,4531,4534],{"style":647},[573,4532],{"className":4533,"style":652},[651],[573,4535,4537],{"className":4536},[656,657,658,659],[573,4538,682],{"className":4539},[624,659],[573,4541],{"className":4542,"style":900},[899],[573,4544,837],{"className":4545},[904],[573,4547],{"className":4548,"style":900},[899],[573,4550,4552,4555],{"className":4551},[615],[573,4553],{"className":4554,"style":1406},[619],[573,4556,601],{"className":4557},[624],[573,4559,4561,4579],{"className":4560},[576],[573,4562,4564],{"className":4563},[580],[582,4565,4566],{"xmlns":584},[586,4567,4568,4576],{},[589,4569,4570,4572,4574],{},[595,4571,597],{},[835,4573,837],{},[599,4575,682],{},[603,4577,4578],{"encoding":605},"x = 2",[573,4580,4582,4600],{"className":4581,"ariaHidden":611},[610],[573,4583,4585,4588,4591,4594,4597],{"className":4584},[615],[573,4586],{"className":4587,"style":811},[619],[573,4589,597],{"className":4590},[624,628],[573,4592],{"className":4593,"style":900},[899],[573,4595,837],{"className":4596},[904],[573,4598],{"className":4599,"style":900},[899],[573,4601,4603,4606],{"className":4602},[615],[573,4604],{"className":4605,"style":1406},[619],[573,4607,682],{"className":4608},[624],[568,4610,4611],{},"oder",[573,4613,4615,4635],{"className":4614},[576],[573,4616,4618],{"className":4617},[580],[582,4619,4620],{"xmlns":584},[586,4621,4622,4632],{},[589,4623,4624,4626,4628,4630],{},[595,4625,597],{},[835,4627,837],{},[835,4629,1773],{},[599,4631,682],{},[603,4633,4634],{"encoding":605},"x = -2",[573,4636,4638,4656],{"className":4637,"ariaHidden":611},[610],[573,4639,4641,4644,4647,4650,4653],{"className":4640},[615],[573,4642],{"className":4643,"style":811},[619],[573,4645,597],{"className":4646},[624,628],[573,4648],{"className":4649,"style":900},[899],[573,4651,837],{"className":4652},[904],[573,4654],{"className":4655,"style":900},[899],[573,4657,4659,4662,4665],{"className":4658},[615],[573,4660],{"className":4661,"style":2201},[619],[573,4663,1773],{"className":4664},[624],[573,4666,682],{"className":4667},[624],[987,4669,4670,4671,4699,4700,4785],{},"Aus einer negativen Lösung ",[573,4672,4674,4687],{"className":4673},[576],[573,4675,4677],{"className":4676},[580],[582,4678,4679],{"xmlns":584},[586,4680,4681,4685],{},[589,4682,4683],{},[595,4684,1066],{},[603,4686,1066],{"encoding":605},[573,4688,4690],{"className":4689,"ariaHidden":611},[610],[573,4691,4693,4696],{"className":4692},[615],[573,4694],{"className":4695,"style":811},[619],[573,4697,1066],{"className":4698,"style":1081},[624,628]," eine Wurzel ziehen wollen. ",[573,4701,4703,4726],{"className":4702},[576],[573,4704,4706],{"className":4705},[580],[582,4707,4708],{"xmlns":584},[586,4709,4710,4724],{},[589,4711,4712,4718,4720,4722],{},[592,4713,4714,4716],{},[595,4715,597],{},[599,4717,682],{},[835,4719,837],{},[835,4721,1773],{},[599,4723,601],{},[603,4725,3651],{"encoding":605},[573,4727,4729,4773],{"className":4728,"ariaHidden":611},[610],[573,4730,4732,4735,4764,4767,4770],{"className":4731},[615],[573,4733],{"className":4734,"style":620},[619],[573,4736,4738,4741],{"className":4737},[624],[573,4739,597],{"className":4740},[624,628],[573,4742,4744],{"className":4743},[632],[573,4745,4747],{"className":4746},[636],[573,4748,4750],{"className":4749},[640],[573,4751,4753],{"className":4752,"style":620},[644],[573,4754,4755,4758],{"style":647},[573,4756],{"className":4757,"style":652},[651],[573,4759,4761],{"className":4760},[656,657,658,659],[573,4762,682],{"className":4763},[624,659],[573,4765],{"className":4766,"style":900},[899],[573,4768,837],{"className":4769},[904],[573,4771],{"className":4772,"style":900},[899],[573,4774,4776,4779,4782],{"className":4775},[615],[573,4777],{"className":4778,"style":2201},[619],[573,4780,1773],{"className":4781},[624],[573,4783,601],{"className":4784},[624]," hat keine reelle Lösung.",[987,4787,4788,4789,4168,4847,4875],{},"Die Substitution bei Gleichungen mit ",[573,4790,4792,4809],{"className":4791},[576],[573,4793,4795],{"className":4794},[580],[582,4796,4797],{"xmlns":584},[586,4798,4799,4807],{},[589,4800,4801],{},[592,4802,4803,4805],{},[595,4804,597],{},[599,4806,743],{},[603,4808,746],{"encoding":605},[573,4810,4812],{"className":4811,"ariaHidden":611},[610],[573,4813,4815,4818],{"className":4814},[615],[573,4816],{"className":4817,"style":620},[619],[573,4819,4821,4824],{"className":4820},[624],[573,4822,597],{"className":4823},[624,628],[573,4825,4827],{"className":4826},[632],[573,4828,4830],{"className":4829},[636],[573,4831,4833],{"className":4832},[640],[573,4834,4836],{"className":4835,"style":620},[644],[573,4837,4838,4841],{"style":647},[573,4839],{"className":4840,"style":652},[651],[573,4842,4844],{"className":4843},[656,657,658,659],[573,4845,743],{"className":4846},[624,659],[573,4848,4850,4863],{"className":4849},[576],[573,4851,4853],{"className":4852},[580],[582,4854,4855],{"xmlns":584},[586,4856,4857,4861],{},[589,4858,4859],{},[595,4860,597],{},[603,4862,597],{"encoding":605},[573,4864,4866],{"className":4865,"ariaHidden":611},[610],[573,4867,4869,4872],{"className":4868},[615],[573,4870],{"className":4871,"style":811},[619],[573,4873,597],{"className":4874},[624,628]," verwenden. Sie funktioniert nur, wenn ausschließlich gerade Potenzen vorkommen.",{"title":4877,"searchDepth":4878,"depth":4878,"links":4879},"",2,[4880,4881,4882],{"id":561,"depth":4878,"text":562},{"id":1798,"depth":4878,"text":1799},{"id":4227,"depth":4878,"text":4228},[4884,4887,4890,4893,4896,4899,4902,4905,4909,4912,4915],{"lhs":4885,"rhs":4886},"a*x^4 + b*x^2 + c","a*(x^2)^2 + b*(x^2) + c",{"lhs":4888,"rhs":4889},"z^2 - 13*z + 36","(z - 4)*(z - 9)",{"lhs":4891,"rhs":1374,"where":4892},"x^4 - 13*x^2 + 36",{"x":4878},{"lhs":4891,"rhs":1374,"where":4894},{"x":4895},-2,{"lhs":4891,"rhs":1374,"where":4897},{"x":4898},3,{"lhs":4891,"rhs":1374,"where":4900},{"x":4901},-3,{"lhs":4903,"rhs":4904},"z^2 + 3*z - 4","(z - 1)*(z + 4)",{"lhs":4906,"rhs":1374,"where":4907},"x^4 + 3*x^2 - 4",{"x":4908},1,{"lhs":4906,"rhs":1374,"where":4910},{"x":4911},-1,{"lhs":4913,"rhs":4914},"2*x^4 - 8*x^2","2*x^2*(x^2 - 4)",{"lhs":4916,"rhs":1374},"2*2^4 - 8*2^2","a \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","biquadratic-equation","ax^4 + bx^2 + c = 0 \\;\\xrightarrow{\\ z = x^2\\ }\\; az^2 + bz + c = 0","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>4\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmover>\u003Cmo stretchy=\"true\" minsize=\"3.0em\">→\u003C\u002Fmo>\u003Cmpadded width=\"+0.6em\" lspace=\"0.3em\">\u003Cmrow>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>z\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmtext> \u003C\u002Fmtext>\u003C\u002Fmrow>\u003C\u002Fmpadded>\u003C\u002Fmover>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>a\u003C\u002Fmi>\u003Cmsup>\u003Cmi>z\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>z\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">ax^4 + bx^2 + c = 0 \\;\\xrightarrow{\\ z = x^2\\ }\\; az^2 + bz + c = 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">4\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2569em;vertical-align:-0.011em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel x-arrow\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2459em;\">\u003Cspan style=\"top:-3.322em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight x-arrow-pad\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mspace mtight\">\u003Cspan class=\"mtight\"> \u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-2.931em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace mtight\">\u003Cspan class=\"mtight\"> \u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"svg-align\" style=\"top:-2.689em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"height:0.522em;min-width:1.469em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"0.522em\" viewBox=\"0 0 400000 522\" preserveAspectRatio=\"xMaxYMin slice\">\u003Cpath d=\"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.011em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Falgebra\u002Fbiquadratische-gleichung",[],[4930,4931,4932,4933],"pq-formula","quadratic-equation-forms","abc-formula","zero-product",{"title":548,"description":4877},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fbiquadratische-gleichung","Eine Gleichung mit nur x⁴, x² und einer Zahl wird mit z = x² zu einer quadratischen Gleichung.",[4938,4939,4940,4941],"substitution","gleichung vierten grades","resubstitution","nullstellen",[4943,4947,4950],{"symbol":4944,"meaning":4945,"symbolHtml":4946},"a, b, c","Koeffizienten, a ist der Faktor vor x⁴","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":597,"meaning":4948,"symbolHtml":4949},"gesuchte Variable","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1066,"meaning":4951,"symbolHtml":4952},"Hilfsvariable, die für x² steht","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>z\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">z\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","vEgsGRHLM-cD5ScDC5QeyrCrPfHDaOTUuqvEHMstaEY",[4955,4958,4961,4964],{"stem":4956,"title":4957,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fabc-formel","abc-Formel (Mitternachtsformel)",{"stem":4959,"title":4960,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fnormalform-quadratische-gleichung","Normalform einer quadratischen Gleichung",{"stem":4962,"title":4963,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fpq-formel","p-q-Formel",{"stem":4965,"title":4966,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fsatz-vom-nullprodukt","Satz vom Nullprodukt",1793824271402]