Issolvi -500000x^2+45x-9*10^-6=0

$$-500000 { x }^{ 2 } +45x-9 \times { 10 }^{ -6 } = 0$$

Solvi għal x

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0.0000898$$

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0.0000002$$

Passi għall-Użu tal-Formula Kwadratika

Ikkalkula 10 bil-power ta' -6 u tikseb \frac{1}{1000000}.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

Immultiplika 9 u \frac{1}{1000000} biex tikseb \frac{9}{1000000}.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi -500000 għal a, 45 għal b, u -\frac{9}{1000000} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-45±\sqrt{45^{2}-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Ikkwadra 45.

$$x=\frac{-45±\sqrt{2025-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Immultiplika -4 b'-500000.

$$x=\frac{-45±\sqrt{2025+2000000\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Immultiplika 2000000 b'-\frac{9}{1000000}.

$$x=\frac{-45±\sqrt{2025-18}}{2\left(-500000\right)}$$

Żid 2025 ma' -18.

$$x=\frac{-45±\sqrt{2007}}{2\left(-500000\right)}$$

Ħu l-għerq kwadrat ta' 2007.

$$x=\frac{-45±3\sqrt{223}}{2\left(-500000\right)}$$

Immultiplika 2 b'-500000.

$$x=\frac{-45±3\sqrt{223}}{-1000000}$$

Issa solvi l-ekwazzjoni x=\frac{-45±3\sqrt{223}}{-1000000} fejn ± hija plus. Żid -45 ma' 3\sqrt{223}.

$$x=\frac{3\sqrt{223}-45}{-1000000}$$

Iddividi -45+3\sqrt{223} b'-1000000.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Issa solvi l-ekwazzjoni x=\frac{-45±3\sqrt{223}}{-1000000} fejn ± hija minus. Naqqas 3\sqrt{223} minn -45.

$$x=\frac{-3\sqrt{223}-45}{-1000000}$$

Iddividi -45-3\sqrt{223} b'-1000000.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

L-ekwazzjoni issa solvuta.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Passi biex Tikkompleta l-Kwadrat

Ikkalkula 10 bil-power ta' -6 u tikseb \frac{1}{1000000}.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

Immultiplika 9 u \frac{1}{1000000} biex tikseb \frac{9}{1000000}.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

Żid \frac{9}{1000000} maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$-500000x^{2}+45x=\frac{9}{1000000}$$

Iddividi ż-żewġ naħat b'-500000.

$$\frac{-500000x^{2}+45x}{-500000}=\frac{\frac{9}{1000000}}{-500000}$$

Meta tiddividi b'-500000 titneħħa l-multiplikazzjoni b'-500000.

$$x^{2}+\frac{45}{-500000}x=\frac{\frac{9}{1000000}}{-500000}$$

Naqqas il-frazzjoni \frac{45}{-500000} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$x^{2}-\frac{9}{100000}x=\frac{\frac{9}{1000000}}{-500000}$$

Iddividi \frac{9}{1000000} b'-500000.

$$x^{2}-\frac{9}{100000}x=-\frac{9}{500000000000}$$

Iddividi -\frac{9}{100000}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{9}{200000}. Imbagħad żid il-kwadru ta' -\frac{9}{200000} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-\frac{9}{100000}x+\left(-\frac{9}{200000}\right)^{2}=-\frac{9}{500000000000}+\left(-\frac{9}{200000}\right)^{2}$$

Ikkwadra -\frac{9}{200000} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=-\frac{9}{500000000000}+\frac{81}{40000000000}$$

Żid -\frac{9}{500000000000} ma' \frac{81}{40000000000} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=\frac{2007}{1000000000000}$$

Fattur x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{9}{200000}\right)^{2}=\frac{2007}{1000000000000}$$

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

$$\sqrt{\left(x-\frac{9}{200000}\right)^{2}}=\sqrt{\frac{2007}{1000000000000}}$$

Issimplifika.

$$x-\frac{9}{200000}=\frac{3\sqrt{223}}{1000000} x-\frac{9}{200000}=-\frac{3\sqrt{223}}{1000000}$$

Żid \frac{9}{200000} maż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$