Réitigh -1800x^2-62000000x-600000000=0

$$-1800 { x }^{ 2 } -62000000x-600000000=0$$

Réitigh do x.

$$x=\frac{13000\sqrt{142}-155000}{9}\approx -9.680139826$$

$$x=\frac{-13000\sqrt{142}-155000}{9}\approx -34434.764304619$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Is féidir gach cothromóid san fhoirm ax^{2}+bx+c=0 a réiteach ag baint úsáid as an bhfoirmle chearnach : \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Tugann an fhoirmle chearnach dhá réiteach, ceann amháin nuair is suimiú é ± agus ceann eile nuair is dealú é.

$$-1800x^{2}-62000000x-600000000=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -1800 in ionad a, -62000000 in ionad b, agus -600000000 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-62000000\right)±\sqrt{\left(-62000000\right)^{2}-4\left(-1800\right)\left(-600000000\right)}}{2\left(-1800\right)}$$

Cearnóg -62000000.

$$x=\frac{-\left(-62000000\right)±\sqrt{3844000000000000-4\left(-1800\right)\left(-600000000\right)}}{2\left(-1800\right)}$$

Méadaigh -4 faoi -1800.

$$x=\frac{-\left(-62000000\right)±\sqrt{3844000000000000+7200\left(-600000000\right)}}{2\left(-1800\right)}$$

Méadaigh 7200 faoi -600000000.

$$x=\frac{-\left(-62000000\right)±\sqrt{3844000000000000-4320000000000}}{2\left(-1800\right)}$$

Suimigh 3844000000000000 le -4320000000000?

$$x=\frac{-\left(-62000000\right)±\sqrt{3839680000000000}}{2\left(-1800\right)}$$

Tóg fréamh chearnach 3839680000000000.

$$x=\frac{-\left(-62000000\right)±5200000\sqrt{142}}{2\left(-1800\right)}$$

Tá 62000000 urchomhairleach le -62000000.

$$x=\frac{62000000±5200000\sqrt{142}}{2\left(-1800\right)}$$

Méadaigh 2 faoi -1800.

$$x=\frac{62000000±5200000\sqrt{142}}{-3600}$$

Réitigh an chothromóid x=\frac{62000000±5200000\sqrt{142}}{-3600} nuair is ionann ± agus plus. Suimigh 62000000 le 5200000\sqrt{142}?

$$x=\frac{5200000\sqrt{142}[phone]}{-3600}$$

Roinn 62000000+5200000\sqrt{142} faoi -3600.

$$x=\frac{-13000\sqrt{142}-155000}{9}$$

Réitigh an chothromóid x=\frac{62000000±5200000\sqrt{142}}{-3600} nuair is ionann ± agus míneas. Dealaigh 5200000\sqrt{142} ó 62000000.

$$x=\frac{62000000-5200000\sqrt{142}}{-3600}$$

Roinn 62000000-5200000\sqrt{142} faoi -3600.

$$x=\frac{13000\sqrt{142}-155000}{9}$$

Tá an chothromóid réitithe anois.

$$x=\frac{-13000\sqrt{142}-155000}{9} x=\frac{13000\sqrt{142}-155000}{9}$$

Céimeanna chun an Chearnóg a Chomhlánú

Is féidir cothromóidí cearnach cosúil leis an gceann seo a réitigh tríd an gcearnóg a chomhlánú. Chun an chearnóg a chomhlánú, ní mór don chothromóid a bheith san fhoirm x^{2}+bx=c ar dtús.

$$-1800x^{2}-62000000x-600000000=0$$

Cuir 600000000 leis an dá thaobh den chothromóid.

$$-1800x^{2}-62000000x-600000000-\left(-600000000\right)=-\left(-600000000\right)$$

Má dhealaítear -600000000 uaidh féin faightear 0.

$$-1800x^{2}-62000000x=-\left(-600000000\right)$$

Dealaigh -600000000 ó 0.

$$-1800x^{2}-62000000x=600000000$$

Roinn an dá thaobh faoi -1800.

$$\frac{-1800x^{2}-62000000x}{-1800}=\frac{600000000}{-1800}$$

Má roinntear é faoi -1800 cuirtear an iolrúchán faoi -1800 ar ceal.

$$x^{2}+\left(-\frac{62000000}{-1800}\right)x=\frac{600000000}{-1800}$$

Laghdaigh an codán \frac{-62000000}{-1800} chuig na téarmaí is ísle trí 200 a bhaint agus a chealú.

$$x^{2}+\frac{310000}{9}x=\frac{600000000}{-1800}$$

Laghdaigh an codán \frac{600000000}{-1800} chuig na téarmaí is ísle trí 600 a bhaint agus a chealú.

$$x^{2}+\frac{310000}{9}x=-\frac{1000000}{3}$$

Roinn \frac{310000}{9}, comhéifeacht an téarma x, faoi 2 chun \frac{155000}{9} a fháil. Ansin suimigh uimhir chearnach \frac{155000}{9} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$x^{2}+\frac{310000}{9}x+\left(\frac{155000}{9}\right)^{2}=-\frac{1000000}{3}+\left(\frac{155000}{9}\right)^{2}$$

Cearnaigh \frac{155000}{9} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$x^{2}+\frac{310000}{9}x+\frac{24025000000}{81}=-\frac{1000000}{3}+\frac{24025000000}{81}$$

Suimigh -\frac{1000000}{3} le \frac{24025000000}{81} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

$$x^{2}+\frac{310000}{9}x+\frac{24025000000}{81}=\frac{23998000000}{81}$$

Fachtóirigh x^{2}+\frac{310000}{9}x+\frac{24025000000}{81}. 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}.

$$\left(x+\frac{155000}{9}\right)^{2}=\frac{23998000000}{81}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(x+\frac{155000}{9}\right)^{2}}=\sqrt{\frac{23998000000}{81}}$$

Simpligh.

$$x+\frac{155000}{9}=\frac{13000\sqrt{142}}{9} x+\frac{155000}{9}=-\frac{13000\sqrt{142}}{9}$$

Bain \frac{155000}{9} ón dá thaobh den chothromóid.

$$x=\frac{13000\sqrt{142}-155000}{9} x=\frac{-13000\sqrt{142}-155000}{9}$$