Réitigh -500000x^2+45x-9*10^-6=0

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

Réitigh do x.

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

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

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Ríomh cumhacht 10 de -6 agus faigh \frac{1}{1000000}.

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

Méadaigh 9 agus \frac{1}{1000000} chun \frac{9}{1000000} a fháil.

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

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -500000 in ionad a, 45 in ionad b, agus -\frac{9}{1000000} in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Cearnóg 45.

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

Méadaigh -4 faoi -500000.

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

Méadaigh 2000000 faoi -\frac{9}{1000000}.

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

Suimigh 2025 le -18?

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

Tóg fréamh chearnach 2007.

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

Méadaigh 2 faoi -500000.

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

Réitigh an chothromóid x=\frac{-45±3\sqrt{223}}{-1000000} nuair is ionann ± agus plus. Suimigh -45 le 3\sqrt{223}?

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

Roinn -45+3\sqrt{223} faoi -1000000.

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

Réitigh an chothromóid x=\frac{-45±3\sqrt{223}}{-1000000} nuair is ionann ± agus míneas. Dealaigh 3\sqrt{223} ó -45.

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

Roinn -45-3\sqrt{223} faoi -1000000.

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

Tá an chothromóid réitithe anois.

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

Céimeanna chun an Chearnóg a Chomhlánú

Ríomh cumhacht 10 de -6 agus faigh \frac{1}{1000000}.

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

Méadaigh 9 agus \frac{1}{1000000} chun \frac{9}{1000000} a fháil.

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

Cuir \frac{9}{1000000} leis an dá thaobh. Is ionann rud ar bith móide nialas agus a shuim féin.

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

Roinn an dá thaobh faoi -500000.

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

Má roinntear é faoi -500000 cuirtear an iolrúchán faoi -500000 ar ceal.

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

Laghdaigh an codán \frac{45}{-500000} chuig na téarmaí is ísle trí 5 a bhaint agus a chealú.

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

Roinn \frac{9}{1000000} faoi -500000.

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

Roinn -\frac{9}{100000}, comhéifeacht an téarma x, faoi 2 chun -\frac{9}{200000} a fháil. Ansin suimigh uimhir chearnach -\frac{9}{200000} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

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

Cearnaigh -\frac{9}{200000} trí uimhreoir agus ainmneoir an chodáin a chearnú.

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

Suimigh -\frac{9}{500000000000} le \frac{81}{40000000000} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

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

Fachtóirigh x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}. Go ginearálta, nuair x^{2}+bx+c cearnóg fhoirfe é, is féidir é a fhachtóiriú i gcónaí mar \left(x+\frac{b}{2}\right)^{2}.

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

Tóg fréamh chearnach an dá thaobh den chothromóid.

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

Simpligh.

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

Cuir \frac{9}{200000} leis an dá thaobh den chothromóid.

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