Réitigh 8p-13+11p^2

$$8 p - 13 + 11 p ^ { 2 }$$

Fachtóirigh

$$11\left(p-\frac{-\sqrt{159}-4}{11}\right)\left(p-\frac{\sqrt{159}-4}{11}\right)$$

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.

$$11p^{2}+8p-13=0$$

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.

$$p=\frac{-8±\sqrt{8^{2}-4\times 11\left(-13\right)}}{2\times 11}$$

Cearnóg 8.

$$p=\frac{-8±\sqrt{64-4\times 11\left(-13\right)}}{2\times 11}$$

Méadaigh -4 faoi 11.

$$p=\frac{-8±\sqrt{64-44\left(-13\right)}}{2\times 11}$$

Méadaigh -44 faoi -13.

$$p=\frac{-8±\sqrt{64+572}}{2\times 11}$$

Suimigh 64 le 572?

$$p=\frac{-8±\sqrt{636}}{2\times 11}$$

Tóg fréamh chearnach 636.

$$p=\frac{-8±2\sqrt{159}}{2\times 11}$$

Méadaigh 2 faoi 11.

$$p=\frac{-8±2\sqrt{159}}{22}$$

Réitigh an chothromóid p=\frac{-8±2\sqrt{159}}{22} nuair is ionann ± agus plus. Suimigh -8 le 2\sqrt{159}?

$$p=\frac{2\sqrt{159}-8}{22}$$

Roinn -8+2\sqrt{159} faoi 22.

$$p=\frac{\sqrt{159}-4}{11}$$

Réitigh an chothromóid p=\frac{-8±2\sqrt{159}}{22} nuair is ionann ± agus míneas. Dealaigh 2\sqrt{159} ó -8.

$$p=\frac{-2\sqrt{159}-8}{22}$$

Roinn -8-2\sqrt{159} faoi 22.

$$p=\frac{-\sqrt{159}-4}{11}$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir \frac{-4+\sqrt{159}}{11} in ionad x_{1} agus \frac{-4-\sqrt{159}}{11} in ionad x_{2}.

$$11p^{2}+8p-13=11\left(p-\frac{\sqrt{159}-4}{11}\right)\left(p-\frac{-\sqrt{159}-4}{11}\right)$$

Luacháil

$$11p^{2}+8p-13$$