Issolvi 5-x/4*10^6=9.6x-x^2

$$\frac { 5 - x } { 4 \times 10 ^ { 6 } } = 9.6 x - x ^ { 2 }$$

Solvi għal x

$$x = \frac{\sqrt{1474559996800001} + 38400001}{8000000} \approx 9.60000012$$

$$x=\frac{38400001-\sqrt{1474559996800001}}{8000000}\approx 0.00000013$$

Passi għall-Użu tal-Formula Kwadratika

Ikkalkula 10 bil-power ta' 6 u tikseb 1000000.

$$\frac{5-x}{4\times 1000000}=9.6x-x^{2}$$

Immultiplika 4 u 1000000 biex tikseb 4000000.

$$\frac{5-x}{4000000}=9.6x-x^{2}$$

Iddividi kull terminu ta' 5-x b'4000000 biex tikseb\frac{1}{800000}-\frac{1}{4000000}x.

$$\frac{1}{800000}-\frac{1}{4000000}x=9.6x-x^{2}$$

Naqqas 9.6x miż-żewġ naħat.

$$\frac{1}{800000}-\frac{1}{4000000}x-9.6x=-x^{2}$$

Ikkombina -\frac{1}{4000000}x u -9.6x biex tikseb -\frac{38400001}{4000000}x.

$$\frac{1}{800000}-\frac{38400001}{4000000}x=-x^{2}$$

Żid x^{2} maż-żewġ naħat.

$$\frac{1}{800000}-\frac{38400001}{4000000}x+x^{2}=0$$

L-ekwazzjonijiet kollha tal-formola ax^{2}+bx+c=0 jistgħu jiġu solvuti permezz tal-formula kwadratika: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Il-formula kwadratika tagħti żewġ soluzzjonijiet, waħda meta ± hija addizzjoni u waħda meta hija tnaqqis.

$$x^{2}-\frac{38400001}{4000000}x+\frac{1}{800000}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 1 għal a, -\frac{38400001}{4000000} għal b, u \frac{1}{800000} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{38400001}{4000000}\right)±\sqrt{\left(-\frac{38400001}{4000000}\right)^{2}-4\times \frac{1}{800000}}}{2}$$

Ikkwadra -\frac{38400001}{4000000} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-\left(-\frac{38400001}{4000000}\right)±\sqrt{\frac{1474560076800001}{16000000000000}-4\times \frac{1}{800000}}}{2}$$

Immultiplika -4 b'\frac{1}{800000}.

$$x=\frac{-\left(-\frac{38400001}{4000000}\right)±\sqrt{\frac{1474560076800001}{16000000000000}-\frac{1}{200000}}}{2}$$

Żid \frac{1474560076800001}{16000000000000} ma' -\frac{1}{200000} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x=\frac{-\left(-\frac{38400001}{4000000}\right)±\sqrt{\frac{1474559996800001}{16000000000000}}}{2}$$

Ħu l-għerq kwadrat ta' \frac{1474559996800001}{16000000000000}.

$$x=\frac{-\left(-\frac{38400001}{4000000}\right)±\frac{\sqrt{1474559996800001}}{4000000}}{2}$$

L-oppost ta' -\frac{38400001}{4000000} huwa \frac{38400001}{4000000}.

$$x=\frac{\frac{38400001}{4000000}±\frac{\sqrt{1474559996800001}}{4000000}}{2}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{38400001}{4000000}±\frac{\sqrt{1474559996800001}}{4000000}}{2} fejn ± hija plus. Żid \frac{38400001}{4000000} ma' \frac{\sqrt{1474559996800001}}{4000000}.

$$x=\frac{\sqrt{1474559996800001}[phone]}{2\times 4000000}$$

Iddividi \frac{38400001+\sqrt{1474559996800001}}{4000000} b'2.

$$x=\frac{\sqrt{1474559996800001}[phone]}{8000000}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{38400001}{4000000}±\frac{\sqrt{1474559996800001}}{4000000}}{2} fejn ± hija minus. Naqqas \frac{\sqrt{1474559996800001}}{4000000} minn \frac{38400001}{4000000}.

$$x=\frac{38400001-\sqrt{1474559996800001}}{2\times 4000000}$$

Iddividi \frac{38400001-\sqrt{1474559996800001}}{4000000} b'2.

$$x=\frac{38400001-\sqrt{1474559996800001}}{8000000}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{\sqrt{1474559996800001}[phone]}{8000000} x=\frac{38400001-\sqrt{1474559996800001}}{8000000}$$

Passi biex Tikkompleta l-Kwadrat

Ikkalkula 10 bil-power ta' 6 u tikseb 1000000.

$$\frac{5-x}{4\times 1000000}=9.6x-x^{2}$$

Immultiplika 4 u 1000000 biex tikseb 4000000.

$$\frac{5-x}{4000000}=9.6x-x^{2}$$

Iddividi kull terminu ta' 5-x b'4000000 biex tikseb\frac{1}{800000}-\frac{1}{4000000}x.

$$\frac{1}{800000}-\frac{1}{4000000}x=9.6x-x^{2}$$

Naqqas 9.6x miż-żewġ naħat.

$$\frac{1}{800000}-\frac{1}{4000000}x-9.6x=-x^{2}$$

Ikkombina -\frac{1}{4000000}x u -9.6x biex tikseb -\frac{38400001}{4000000}x.

$$\frac{1}{800000}-\frac{38400001}{4000000}x=-x^{2}$$

Żid x^{2} maż-żewġ naħat.

$$\frac{1}{800000}-\frac{38400001}{4000000}x+x^{2}=0$$

Naqqas \frac{1}{800000} miż-żewġ naħat. Xi ħaġa mnaqqsa minn żero tagħti numru negattiv.

$$-\frac{38400001}{4000000}x+x^{2}=-\frac{1}{800000}$$

Ekwazzjonijiet kwadratiċi bħal din jistgħu jiġu solvuti billi tikkompleta l-kwadrat. Sabiex tikkompleta l-kwadrat, l-ekwazzjoni l-ewwel trid tkun fil-forma x^{2}+bx=c.

$$x^{2}-\frac{38400001}{4000000}x=-\frac{1}{800000}$$

Iddividi -\frac{38400001}{4000000}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{38400001}{8000000}. Imbagħad żid il-kwadru ta' -\frac{38400001}{8000000} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-\frac{38400001}{4000000}x+\left(-\frac{38400001}{8000000}\right)^{2}=-\frac{1}{800000}+\left(-\frac{38400001}{8000000}\right)^{2}$$

Ikkwadra -\frac{38400001}{8000000} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}-\frac{38400001}{4000000}x+\frac{1474560076800001}{64000000000000}=-\frac{1}{800000}+\frac{1474560076800001}{64000000000000}$$

Żid -\frac{1}{800000} ma' \frac{1474560076800001}{64000000000000} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}-\frac{38400001}{4000000}x+\frac{1474560076800001}{64000000000000}=\frac{1474559996800001}{64000000000000}$$

Fattur x^{2}-\frac{38400001}{4000000}x+\frac{1474560076800001}{64000000000000}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{38400001}{8000000}\right)^{2}=\frac{1474559996800001}{64000000000000}$$

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

$$\sqrt{\left(x-\frac{38400001}{8000000}\right)^{2}}=\sqrt{\frac{1474559996800001}{64000000000000}}$$

Issimplifika.

$$x-\frac{38400001}{8000000}=\frac{\sqrt{1474559996800001}}{8000000} x-\frac{38400001}{8000000}=-\frac{\sqrt{1474559996800001}}{8000000}$$

Żid \frac{38400001}{8000000} maż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{\sqrt{1474559996800001}[phone]}{8000000} x=\frac{38400001-\sqrt{1474559996800001}}{8000000}$$