Réitigh 301+2t^2=300t

$$301 + 2 t ^ { 2 } = 300 t$$

Réitigh do t.

$$t=\frac{\sqrt{21898}}{2}+75\approx 148.989864171$$

$$t=-\frac{\sqrt{21898}}{2}+75\approx 1.010135829$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Bain 300t ón dá thaobh.

$$301+2t^{2}-300t=0$$

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.

$$2t^{2}-300t+301=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 2 in ionad a, -300 in ionad b, agus 301 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-300\right)±\sqrt{\left(-300\right)^{2}-4\times 2\times 301}}{2\times 2}$$

Cearnóg -300.

$$t=\frac{-\left(-300\right)±\sqrt{90000-4\times 2\times 301}}{2\times 2}$$

Méadaigh -4 faoi 2.

$$t=\frac{-\left(-300\right)±\sqrt{90000-8\times 301}}{2\times 2}$$

Méadaigh -8 faoi 301.

$$t=\frac{-\left(-300\right)±\sqrt{90000-2408}}{2\times 2}$$

Suimigh 90000 le -2408?

$$t=\frac{-\left(-300\right)±\sqrt{87592}}{2\times 2}$$

Tóg fréamh chearnach 87592.

$$t=\frac{-\left(-300\right)±2\sqrt{21898}}{2\times 2}$$

Tá 300 urchomhairleach le -300.

$$t=\frac{300±2\sqrt{21898}}{2\times 2}$$

Méadaigh 2 faoi 2.

$$t=\frac{300±2\sqrt{21898}}{4}$$

Réitigh an chothromóid t=\frac{300±2\sqrt{21898}}{4} nuair is ionann ± agus plus. Suimigh 300 le 2\sqrt{21898}?

$$t=\frac{2\sqrt{21898}+300}{4}$$

Roinn 300+2\sqrt{21898} faoi 4.

$$t=\frac{\sqrt{21898}}{2}+75$$

Réitigh an chothromóid t=\frac{300±2\sqrt{21898}}{4} nuair is ionann ± agus míneas. Dealaigh 2\sqrt{21898} ó 300.

$$t=\frac{300-2\sqrt{21898}}{4}$$

Roinn 300-2\sqrt{21898} faoi 4.

$$t=-\frac{\sqrt{21898}}{2}+75$$

Tá an chothromóid réitithe anois.

$$t=\frac{\sqrt{21898}}{2}+75 t=-\frac{\sqrt{21898}}{2}+75$$

Céimeanna chun an Chearnóg a Chomhlánú

Bain 300t ón dá thaobh.

$$301+2t^{2}-300t=0$$

Bain 301 ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$2t^{2}-300t=-301$$

Roinn an dá thaobh faoi 2.

$$\frac{2t^{2}-300t}{2}=-\frac{301}{2}$$

Má roinntear é faoi 2 cuirtear an iolrúchán faoi 2 ar ceal.

$$t^{2}+\left(-\frac{300}{2}\right)t=-\frac{301}{2}$$

Roinn -300 faoi 2.

$$t^{2}-150t=-\frac{301}{2}$$

Roinn -150, comhéifeacht an téarma x, faoi 2 chun -75 a fháil. Ansin suimigh uimhir chearnach -75 leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$t^{2}-150t+\left(-75\right)^{2}=-\frac{301}{2}+\left(-75\right)^{2}$$

Cearnóg -75.

$$t^{2}-150t+5625=-\frac{301}{2}+5625$$

Suimigh -\frac{301}{2} le 5625?

$$t^{2}-150t+5625=\frac{10949}{2}$$

Fachtóirigh t^{2}-150t+5625. Go ginearálta, nuair is slánchearnóg é x^{2}+bx+c, is féidir é a fhachtóiriú i gcónaí mar \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-75\right)^{2}=\frac{10949}{2}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(t-75\right)^{2}}=\sqrt{\frac{10949}{2}}$$

Simpligh.

$$t-75=\frac{\sqrt{21898}}{2} t-75=-\frac{\sqrt{21898}}{2}$$

Cuir 75 leis an dá thaobh den chothromóid.

$$t=\frac{\sqrt{21898}}{2}+75 t=-\frac{\sqrt{21898}}{2}+75$$