Whakaoti i te 5b^2-14b-65

$$5 { b }^{ 2 } -14b-65$$

Tauwehe

$$5\left(b-\frac{7-\sqrt{374}}{5}\right)\left(b-\frac{\sqrt{374}+7}{5}\right)$$

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.

$$5b^{2}-14b-65=0$$

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.

$$b=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 5\left(-65\right)}}{2\times 5}$$

Pūrua -14.

$$b=\frac{-\left(-14\right)±\sqrt{196-4\times 5\left(-65\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$b=\frac{-\left(-14\right)±\sqrt{196-20\left(-65\right)}}{2\times 5}$$

Whakareatia -20 ki te -65.

$$b=\frac{-\left(-14\right)±\sqrt{196+1300}}{2\times 5}$$

Tāpiri 196 ki te 1300.

$$b=\frac{-\left(-14\right)±\sqrt{1496}}{2\times 5}$$

Tuhia te pūtakerua o te 1496.

$$b=\frac{-\left(-14\right)±2\sqrt{374}}{2\times 5}$$

Ko te tauaro o -14 ko 14.

$$b=\frac{14±2\sqrt{374}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$b=\frac{14±2\sqrt{374}}{10}$$

Nā, me whakaoti te whārite b=\frac{14±2\sqrt{374}}{10} ina he tāpiri te ±. Tāpiri 14 ki te 2\sqrt{374}.

$$b=\frac{2\sqrt{374}+14}{10}$$

Whakawehe 14+2\sqrt{374} ki te 10.

$$b=\frac{\sqrt{374}+7}{5}$$

Nā, me whakaoti te whārite b=\frac{14±2\sqrt{374}}{10} ina he tango te ±. Tango 2\sqrt{374} mai i 14.

$$b=\frac{14-2\sqrt{374}}{10}$$

Whakawehe 14-2\sqrt{374} ki te 10.

$$b=\frac{7-\sqrt{374}}{5}$$

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{7+\sqrt{374}}{5} mō te x_{1} me te \frac{7-\sqrt{374}}{5} mō te x_{2}.

$$5b^{2}-14b-65=5\left(b-\frac{\sqrt{374}+7}{5}\right)\left(b-\frac{7-\sqrt{374}}{5}\right)$$

Aromātai

$$5b^{2}-14b-65$$