Réitigh 2p^2-2400000p+7000000

$$2 p ^ { 2 } - 2400000 p + 7000000$$

Fachtóirigh

$$2\left(p-\left(600000-500\sqrt{1439986}\right)\right)\left(p-\left(500\sqrt{1439986}+600000\right)\right)$$

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.

$$2p^{2}-2400000p+7000000=0$$

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.

$$p=\frac{-\left(-2400000\right)±\sqrt{\left(-2400000\right)^{2}-4\times 2\times 7000000}}{2\times 2}$$

Cearnóg -2400000.

$$p=\frac{-\left(-2400000\right)±\sqrt{5760000000000-4\times 2\times 7000000}}{2\times 2}$$

Méadaigh -4 faoi 2.

$$p=\frac{-\left(-2400000\right)±\sqrt{5760000000000-8\times 7000000}}{2\times 2}$$

Méadaigh -8 faoi 7000000.

$$p=\frac{-\left(-2400000\right)±\sqrt{5760000000000-56000000}}{2\times 2}$$

Suimigh 5760000000000 le -56000000?

$$p=\frac{-\left(-2400000\right)±\sqrt{5759944000000}}{2\times 2}$$

Tóg fréamh chearnach 5759944000000.

$$p=\frac{-\left(-2400000\right)±2000\sqrt{1439986}}{2\times 2}$$

Tá 2400000 urchomhairleach le -2400000.

$$p=\frac{2400000±2000\sqrt{1439986}}{2\times 2}$$

Méadaigh 2 faoi 2.

$$p=\frac{2400000±2000\sqrt{1439986}}{4}$$

Réitigh an chothromóid p=\frac{2400000±2000\sqrt{1439986}}{4} nuair is ionann ± agus plus. Suimigh 2400000 le 2000\sqrt{1439986}?

$$p=\frac{2000\sqrt{1439986}+2400000}{4}$$

Roinn 2400000+2000\sqrt{1439986} faoi 4.

$$p=500\sqrt{1439986}+600000$$

Réitigh an chothromóid p=\frac{2400000±2000\sqrt{1439986}}{4} nuair is ionann ± agus míneas. Dealaigh 2000\sqrt{1439986} ó 2400000.

$$p=\frac{2400000-2000\sqrt{1439986}}{4}$$

Roinn 2400000-2000\sqrt{1439986} faoi 4.

$$p=600000-500\sqrt{1439986}$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir 600000+500\sqrt{1439986} in ionad x_{1} agus 600000-500\sqrt{1439986} in ionad x_{2}.

$$2p^{2}-2400000p+7000000=2\left(p-\left(500\sqrt{1439986}+600000\right)\right)\left(p-\left(600000-500\sqrt{1439986}\right)\right)$$

Luacháil

$$2\left(p^{2}-1200000p+3500000\right)$$