Whakaoti i te 5x^2-70x+238

$$5 x ^ { 2 } - 70 x + 238$$

Tauwehe

$$5\left(x-\left(-\frac{\sqrt{35}}{5}+7\right)\right)\left(x-\left(\frac{\sqrt{35}}{5}+7\right)\right)$$

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.

$$5x^{2}-70x+238=0$$

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.

$$x=\frac{-\left(-70\right)±\sqrt{\left(-70\right)^{2}-4\times 5\times 238}}{2\times 5}$$

Pūrua -70.

$$x=\frac{-\left(-70\right)±\sqrt{4900-4\times 5\times 238}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-70\right)±\sqrt{4900-20\times 238}}{2\times 5}$$

Whakareatia -20 ki te 238.

$$x=\frac{-\left(-70\right)±\sqrt{4900-4760}}{2\times 5}$$

Tāpiri 4900 ki te -4760.

$$x=\frac{-\left(-70\right)±\sqrt{140}}{2\times 5}$$

Tuhia te pūtakerua o te 140.

$$x=\frac{-\left(-70\right)±2\sqrt{35}}{2\times 5}$$

Ko te tauaro o -70 ko 70.

$$x=\frac{70±2\sqrt{35}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{70±2\sqrt{35}}{10}$$

Nā, me whakaoti te whārite x=\frac{70±2\sqrt{35}}{10} ina he tāpiri te ±. Tāpiri 70 ki te 2\sqrt{35}.

$$x=\frac{2\sqrt{35}+70}{10}$$

Whakawehe 70+2\sqrt{35} ki te 10.

$$x=\frac{\sqrt{35}}{5}+7$$

Nā, me whakaoti te whārite x=\frac{70±2\sqrt{35}}{10} ina he tango te ±. Tango 2\sqrt{35} mai i 70.

$$x=\frac{70-2\sqrt{35}}{10}$$

Whakawehe 70-2\sqrt{35} ki te 10.

$$x=-\frac{\sqrt{35}}{5}+7$$

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 7+\frac{\sqrt{35}}{5} mō te x_{1} me te 7-\frac{\sqrt{35}}{5} mō te x_{2}.

$$5x^{2}-70x+238=5\left(x-\left(\frac{\sqrt{35}}{5}+7\right)\right)\left(x-\left(-\frac{\sqrt{35}}{5}+7\right)\right)$$

Aromātai

$$5x^{2}-70x+238$$