Réitigh h(t)=-16t^2+416t+32

$$h ( t ) = - 16 t ^ { 2 } + 416 t + 32$$

Fachtóirigh

$$-16\left(t-\left(13-3\sqrt{19}\right)\right)\left(t-\left(3\sqrt{19}+13\right)\right)$$

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.

$$-16t^{2}+416t+32=0$$

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.

$$t=\frac{-416±\sqrt{416^{2}-4\left(-16\right)\times 32}}{2\left(-16\right)}$$

Cearnóg 416.

$$t=\frac{-416±\sqrt{173056-4\left(-16\right)\times 32}}{2\left(-16\right)}$$

Méadaigh -4 faoi -16.

$$t=\frac{-416±\sqrt{173056+64\times 32}}{2\left(-16\right)}$$

Méadaigh 64 faoi 32.

$$t=\frac{-416±\sqrt{173056+2048}}{2\left(-16\right)}$$

Suimigh 173056 le 2048?

$$t=\frac{-416±\sqrt{175104}}{2\left(-16\right)}$$

Tóg fréamh chearnach 175104.

$$t=\frac{-416±96\sqrt{19}}{2\left(-16\right)}$$

Méadaigh 2 faoi -16.

$$t=\frac{-416±96\sqrt{19}}{-32}$$

Réitigh an chothromóid t=\frac{-416±96\sqrt{19}}{-32} nuair is ionann ± agus plus. Suimigh -416 le 96\sqrt{19}?

$$t=\frac{96\sqrt{19}-416}{-32}$$

Roinn -416+96\sqrt{19} faoi -32.

$$t=13-3\sqrt{19}$$

Réitigh an chothromóid t=\frac{-416±96\sqrt{19}}{-32} nuair is ionann ± agus míneas. Dealaigh 96\sqrt{19} ó -416.

$$t=\frac{-96\sqrt{19}-416}{-32}$$

Roinn -416-96\sqrt{19} faoi -32.

$$t=3\sqrt{19}+13$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir 13-3\sqrt{19} in ionad x_{1} agus 13+3\sqrt{19} in ionad x_{2}.

$$-16t^{2}+416t+32=-16\left(t-\left(13-3\sqrt{19}\right)\right)\left(t-\left(3\sqrt{19}+13\right)\right)$$

Luacháil

$$32+416t-16t^{2}$$