Whakaoti i te 8p-13+11p^2

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

Tauwehe

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

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.

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

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.

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

Pūrua 8.

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

Whakareatia -4 ki te 11.

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

Whakareatia -44 ki te -13.

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

Tāpiri 64 ki te 572.

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

Tuhia te pūtakerua o te 636.

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

Whakareatia 2 ki te 11.

$$p=\frac{-8±2\sqrt{159}}{22}$$

Nā, me whakaoti te whārite p=\frac{-8±2\sqrt{159}}{22} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{159}.

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

Whakawehe -8+2\sqrt{159} ki te 22.

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

Nā, me whakaoti te whārite p=\frac{-8±2\sqrt{159}}{22} ina he tango te ±. Tango 2\sqrt{159} mai i -8.

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

Whakawehe -8-2\sqrt{159} ki te 22.

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

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 \frac{-4+\sqrt{159}}{11} mō te x_{1} me te \frac{-4-\sqrt{159}}{11} mō te x_{2}.

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

Aromātai

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