Issolvi x^2/308-x=83176*10^-5

$$\frac{ { x }^{ 2 } }{ 308-x } = 83176 \times { 10 }^{ -5 }$$

Solvi għal x

$$x = \frac{\sqrt{160221897609} - 10397}{25000} \approx 15.595211036$$

$$x=\frac{-\sqrt{160221897609}-10397}{25000}\approx -16.426971036$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal 308 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'-x+308.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

Ikkalkula 10 bil-power ta' -5 u tikseb \frac{1}{100000}.

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

Immultiplika 83176 u \frac{1}{100000} biex tikseb \frac{10397}{12500}.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{10397}{12500} b'-x+308.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

Żid \frac{10397}{12500}x maż-żewġ naħat.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

Naqqas \frac{800569}{3125} miż-żewġ naħat.

$$x^{2}+\frac{10397}{12500}x-\frac{800569}{3125}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 1 għal a, \frac{10397}{12500} għal b, u -\frac{800569}{3125} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\left(\frac{10397}{12500}\right)^{2}-4\left(-\frac{800569}{3125}\right)}}{2}$$

Ikkwadra \frac{10397}{12500} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}-4\left(-\frac{800569}{3125}\right)}}{2}$$

Immultiplika -4 b'-\frac{800569}{3125}.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}+\frac{3202276}{3125}}}{2}$$

Żid \frac{108097609}{156250000} ma' \frac{3202276}{3125} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{160221897609}{156250000}}}{2}$$

Ħu l-għerq kwadrat ta' \frac{160221897609}{156250000}.

$$x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2}$$

Issa solvi l-ekwazzjoni x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} fejn ± hija plus. Żid -\frac{10397}{12500} ma' \frac{\sqrt{160221897609}}{12500}.

$$x=\frac{\sqrt{160221897609}-10397}{2\times 12500}$$

Iddividi \frac{-10397+\sqrt{160221897609}}{12500} b'2.

$$x=\frac{\sqrt{160221897609}-10397}{25000}$$

Issa solvi l-ekwazzjoni x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} fejn ± hija minus. Naqqas \frac{\sqrt{160221897609}}{12500} minn -\frac{10397}{12500}.

$$x=\frac{-\sqrt{160221897609}-10397}{2\times 12500}$$

Iddividi \frac{-10397-\sqrt{160221897609}}{12500} b'2.

$$x=\frac{-\sqrt{160221897609}-10397}{25000}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal 308 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'-x+308.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

Ikkalkula 10 bil-power ta' -5 u tikseb \frac{1}{100000}.

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

Immultiplika 83176 u \frac{1}{100000} biex tikseb \frac{10397}{12500}.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{10397}{12500} b'-x+308.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

Żid \frac{10397}{12500}x maż-żewġ naħat.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

Iddividi \frac{10397}{12500}, il-koeffiċjent tat-terminu x, b'2 biex tikseb \frac{10397}{25000}. Imbagħad żid il-kwadru ta' \frac{10397}{25000} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}+\frac{10397}{12500}x+\left(\frac{10397}{25000}\right)^{2}=\frac{800569}{3125}+\left(\frac{10397}{25000}\right)^{2}$$

Ikkwadra \frac{10397}{25000} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{800569}{3125}+\frac{108097609}{625000000}$$

Żid \frac{800569}{3125} ma' \frac{108097609}{625000000} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{160221897609}{625000000}$$

Fattur x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{10397}{25000}\right)^{2}=\frac{160221897609}{625000000}$$

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

$$\sqrt{\left(x+\frac{10397}{25000}\right)^{2}}=\sqrt{\frac{160221897609}{625000000}}$$

Issimplifika.

$$x+\frac{10397}{25000}=\frac{\sqrt{160221897609}}{25000} x+\frac{10397}{25000}=-\frac{\sqrt{160221897609}}{25000}$$

Naqqas \frac{10397}{25000} miż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$