Whakaoti i te 2p^2-2400000p+7000000

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

Tauwehe

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

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

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

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

Pūrua -2400000.

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

Whakareatia -4 ki te 2.

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

Whakareatia -8 ki te 7000000.

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

Tāpiri 5760000000000 ki te -56000000.

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

Tuhia te pūtakerua o te 5759944000000.

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

Ko te tauaro o -2400000 ko 2400000.

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

Whakareatia 2 ki te 2.

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

Nā, me whakaoti te whārite p=\frac{2400000±2000\sqrt{1439986}}{4} ina he tāpiri te ±. Tāpiri 2400000 ki te 2000\sqrt{1439986}.

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

Whakawehe 2400000+2000\sqrt{1439986} ki te 4.

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

Nā, me whakaoti te whārite p=\frac{2400000±2000\sqrt{1439986}}{4} ina he tango te ±. Tango 2000\sqrt{1439986} mai i 2400000.

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

Whakawehe 2400000-2000\sqrt{1439986} ki te 4.

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

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 600000+500\sqrt{1439986} mō te x_{1} me te 600000-500\sqrt{1439986} mō te x_{2}.

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

Aromātai

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