Réitigh -5t^2+30t+8

$$- 5 t ^ { 2 } + 30 t + 8$$

Fachtóirigh

$$-5\left(t-\left(-\frac{\sqrt{265}}{5}+3\right)\right)\left(t-\left(\frac{\sqrt{265}}{5}+3\right)\right)$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Is féidir an trasfhoirmiú ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) a úsáid chun luach iltéarmach cearnach a fhachtóiriú, nuair is réitigh iad x_{1} agus x_{2} ar an gcothromóid chearnach ax^{2}+bx+c=0.

$$-5t^{2}+30t+8=0$$

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.

$$t=\frac{-30±\sqrt{30^{2}-4\left(-5\right)\times 8}}{2\left(-5\right)}$$

Cearnóg 30.

$$t=\frac{-30±\sqrt{900-4\left(-5\right)\times 8}}{2\left(-5\right)}$$

Méadaigh -4 faoi -5.

$$t=\frac{-30±\sqrt{900+20\times 8}}{2\left(-5\right)}$$

Méadaigh 20 faoi 8.

$$t=\frac{-30±\sqrt{900+160}}{2\left(-5\right)}$$

Suimigh 900 le 160?

$$t=\frac{-30±\sqrt{1060}}{2\left(-5\right)}$$

Tóg fréamh chearnach 1060.

$$t=\frac{-30±2\sqrt{265}}{2\left(-5\right)}$$

Méadaigh 2 faoi -5.

$$t=\frac{-30±2\sqrt{265}}{-10}$$

Réitigh an chothromóid t=\frac{-30±2\sqrt{265}}{-10} nuair is ionann ± agus plus. Suimigh -30 le 2\sqrt{265}?

$$t=\frac{2\sqrt{265}-30}{-10}$$

Roinn -30+2\sqrt{265} faoi -10.

$$t=-\frac{\sqrt{265}}{5}+3$$

Réitigh an chothromóid t=\frac{-30±2\sqrt{265}}{-10} nuair is ionann ± agus míneas. Dealaigh 2\sqrt{265} ó -30.

$$t=\frac{-2\sqrt{265}-30}{-10}$$

Roinn -30-2\sqrt{265} faoi -10.

$$t=\frac{\sqrt{265}}{5}+3$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir 3-\frac{\sqrt{265}}{5} in ionad x_{1} agus 3+\frac{\sqrt{265}}{5} in ionad x_{2}.

$$-5t^{2}+30t+8=-5\left(t-\left(-\frac{\sqrt{265}}{5}+3\right)\right)\left(t-\left(\frac{\sqrt{265}}{5}+3\right)\right)$$

Luacháil

$$8+30t-5t^{2}$$