Réitigh -18y^2-620000y-600000000=0

$$- 18 y ^ { 2 } - 620000 y - 600000000 = 0$$

Réitigh do y.

$$y=\frac{5000\sqrt{853}-155000}{9}\approx -996.575703878$$

$$y=\frac{-5000\sqrt{853}-155000}{9}\approx -33447.868740567$$

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.

$$-18y^{2}-620000y-600000000=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -18 in ionad a, -620000 in ionad b, agus -600000000 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-620000\right)±\sqrt{\left(-620000\right)^{2}-4\left(-18\right)\left(-600000000\right)}}{2\left(-18\right)}$$

Cearnóg -620000.

$$y=\frac{-\left(-620000\right)±\sqrt{384400000000-4\left(-18\right)\left(-600000000\right)}}{2\left(-18\right)}$$

Méadaigh -4 faoi -18.

$$y=\frac{-\left(-620000\right)±\sqrt{384400000000+72\left(-600000000\right)}}{2\left(-18\right)}$$

Méadaigh 72 faoi -600000000.

$$y=\frac{-\left(-620000\right)±\sqrt{384400000000-43200000000}}{2\left(-18\right)}$$

Suimigh 384400000000 le -43200000000?

$$y=\frac{-\left(-620000\right)±\sqrt{341200000000}}{2\left(-18\right)}$$

Tóg fréamh chearnach 341200000000.

$$y=\frac{-\left(-620000\right)±20000\sqrt{853}}{2\left(-18\right)}$$

Tá 620000 urchomhairleach le -620000.

$$y=\frac{620000±20000\sqrt{853}}{2\left(-18\right)}$$

Méadaigh 2 faoi -18.

$$y=\frac{620000±20000\sqrt{853}}{-36}$$

Réitigh an chothromóid y=\frac{620000±20000\sqrt{853}}{-36} nuair is ionann ± agus plus. Suimigh 620000 le 20000\sqrt{853}?

$$y=\frac{20000\sqrt{853}+620000}{-36}$$

Roinn 620000+20000\sqrt{853} faoi -36.

$$y=\frac{-5000\sqrt{853}-155000}{9}$$

Réitigh an chothromóid y=\frac{620000±20000\sqrt{853}}{-36} nuair is ionann ± agus míneas. Dealaigh 20000\sqrt{853} ó 620000.

$$y=\frac{620000-20000\sqrt{853}}{-36}$$

Roinn 620000-20000\sqrt{853} faoi -36.

$$y=\frac{5000\sqrt{853}-155000}{9}$$

Tá an chothromóid réitithe anois.

$$y=\frac{-5000\sqrt{853}-155000}{9} y=\frac{5000\sqrt{853}-155000}{9}$$

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.

$$-18y^{2}-620000y-600000000=0$$

Cuir 600000000 leis an dá thaobh den chothromóid.

$$-18y^{2}-620000y-600000000-\left(-600000000\right)=-\left(-600000000\right)$$

Má dhealaítear -600000000 uaidh féin faightear 0.

$$-18y^{2}-620000y=-\left(-600000000\right)$$

Dealaigh -600000000 ó 0.

$$-18y^{2}-620000y=600000000$$

Roinn an dá thaobh faoi -18.

$$\frac{-18y^{2}-620000y}{-18}=\frac{600000000}{-18}$$

Má roinntear é faoi -18 cuirtear an iolrúchán faoi -18 ar ceal.

$$y^{2}+\left(-\frac{620000}{-18}\right)y=\frac{600000000}{-18}$$

Laghdaigh an codán \frac{-620000}{-18} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$y^{2}+\frac{310000}{9}y=\frac{600000000}{-18}$$

Laghdaigh an codán \frac{600000000}{-18} chuig na téarmaí is ísle trí 6 a bhaint agus a chealú.

$$y^{2}+\frac{310000}{9}y=-\frac{100000000}{3}$$

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.

$$y^{2}+\frac{310000}{9}y+\left(\frac{155000}{9}\right)^{2}=-\frac{100000000}{3}+\left(\frac{155000}{9}\right)^{2}$$

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

$$y^{2}+\frac{310000}{9}y+\frac{24025000000}{81}=-\frac{100000000}{3}+\frac{24025000000}{81}$$

Suimigh -\frac{100000000}{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.

$$y^{2}+\frac{310000}{9}y+\frac{24025000000}{81}=\frac{21325000000}{81}$$

Fachtóirigh y^{2}+\frac{310000}{9}y+\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}.

$$\left(y+\frac{155000}{9}\right)^{2}=\frac{21325000000}{81}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(y+\frac{155000}{9}\right)^{2}}=\sqrt{\frac{21325000000}{81}}$$

Simpligh.

$$y+\frac{155000}{9}=\frac{5000\sqrt{853}}{9} y+\frac{155000}{9}=-\frac{5000\sqrt{853}}{9}$$

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

$$y=\frac{5000\sqrt{853}-155000}{9} y=\frac{-5000\sqrt{853}-155000}{9}$$