Issolvi lambda^2-4999001lambda/100000+0000225=0

$$\lambda ^ { 2 } - \frac { 4999001 \lambda } { 100000 } + 0000225 = 0$$

Solvi għal λ

$$\lambda =\frac{4999001}{100000}=49.99001$$

$$\lambda =0$$

Passi li jużaw il-Fatturar

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'100000.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

Immultiplika 0 u 225 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$100000\lambda ^{2}-4999001\lambda =0$$

Iffattura 'l barra \lambda .

$$\lambda \left(100000\lambda -4999001\right)=0$$

Biex issib soluzzjonijiet tal-ekwazzjoni, solvi \lambda =0 u 100000\lambda -4999001=0.

$$\lambda =0 \lambda =\frac{4999001}{100000}$$

Passi għall-Użu tal-Formula Kwadratika

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'100000.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

Immultiplika 0 u 225 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$100000\lambda ^{2}-4999001\lambda =0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 100000 għal a, -4999001 għal b, u 0 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\lambda =\frac{-\left(-4999001\right)±\sqrt{\left(-4999001\right)^{2}}}{2\times 100000}$$

Ħu l-għerq kwadrat ta' \left(-4999001\right)^{2}.

$$\lambda =\frac{-\left(-4999001\right)±4999001}{2\times 100000}$$

L-oppost ta' -4999001 huwa 4999001.

$$\lambda =\frac{4999001±4999001}{2\times 100000}$$

Immultiplika 2 b'100000.

$$\lambda =\frac{4999001±4999001}{200000}$$

Issa solvi l-ekwazzjoni \lambda =\frac{4999001±4999001}{200000} fejn ± hija plus. Żid 4999001 ma' 4999001.

$$\lambda =\frac{9998002}{200000}$$

Naqqas il-frazzjoni \frac{9998002}{200000} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\lambda =\frac{4999001}{100000}$$

Issa solvi l-ekwazzjoni \lambda =\frac{4999001±4999001}{200000} fejn ± hija minus. Naqqas 4999001 minn 4999001.

$$\lambda =\frac{0}{200000}$$

Iddividi 0 b'200000.

$$\lambda =0$$

L-ekwazzjoni issa solvuta.

$$\lambda =\frac{4999001}{100000} \lambda =0$$

Passi biex Tikkompleta l-Kwadrat

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'100000.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 0\times 225=0$$

Immultiplika 0 u 0 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0\times 225=0$$

Immultiplika 0 u 225 biex tikseb 0.

$$100000\lambda ^{2}-4999001\lambda +0=0$$

Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$100000\lambda ^{2}-4999001\lambda =0$$

Iddividi ż-żewġ naħat b'100000.

$$\frac{100000\lambda ^{2}-4999001\lambda }{100000}=\frac{0}{100000}$$

Meta tiddividi b'100000 titneħħa l-multiplikazzjoni b'100000.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda =\frac{0}{100000}$$

Iddividi 0 b'100000.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda =0$$

Iddividi -\frac{4999001}{100000}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{4999001}{200000}. Imbagħad żid il-kwadru ta' -\frac{4999001}{200000} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda +\left(-\frac{4999001}{200000}\right)^{2}=\left(-\frac{4999001}{200000}\right)^{2}$$

Ikkwadra -\frac{4999001}{200000} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$\lambda ^{2}-\frac{4999001}{100000}\lambda +\frac{24990010998001}{40000000000}=\frac{24990010998001}{40000000000}$$

Fattur \lambda ^{2}-\frac{4999001}{100000}\lambda +\frac{24990010998001}{40000000000}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(\lambda -\frac{4999001}{200000}\right)^{2}=\frac{24990010998001}{40000000000}$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$\sqrt{\left(\lambda -\frac{4999001}{200000}\right)^{2}}=\sqrt{\frac{24990010998001}{40000000000}}$$

Issimplifika.

$$\lambda -\frac{4999001}{200000}=\frac{4999001}{200000} \lambda -\frac{4999001}{200000}=-\frac{4999001}{200000}$$

Żid \frac{4999001}{200000} maż-żewġ naħat tal-ekwazzjoni.

$$\lambda =\frac{4999001}{100000} \lambda =0$$