Whakaoti i te 5x^2-32x+2

$$5 { x }^{ 2 } -32x+2$$

Tauwehe

$$5\left(x-\frac{16-\sqrt{246}}{5}\right)\left(x-\frac{\sqrt{246}+16}{5}\right)$$

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.

$$5x^{2}-32x+2=0$$

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.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\times 5\times 2}}{2\times 5}$$

Pūrua -32.

$$x=\frac{-\left(-32\right)±\sqrt{1024-4\times 5\times 2}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-32\right)±\sqrt{1024-20\times 2}}{2\times 5}$$

Whakareatia -20 ki te 2.

$$x=\frac{-\left(-32\right)±\sqrt{1024-40}}{2\times 5}$$

Tāpiri 1024 ki te -40.

$$x=\frac{-\left(-32\right)±\sqrt{984}}{2\times 5}$$

Tuhia te pūtakerua o te 984.

$$x=\frac{-\left(-32\right)±2\sqrt{246}}{2\times 5}$$

Ko te tauaro o -32 ko 32.

$$x=\frac{32±2\sqrt{246}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{32±2\sqrt{246}}{10}$$

Nā, me whakaoti te whārite x=\frac{32±2\sqrt{246}}{10} ina he tāpiri te ±. Tāpiri 32 ki te 2\sqrt{246}.

$$x=\frac{2\sqrt{246}+32}{10}$$

Whakawehe 32+2\sqrt{246} ki te 10.

$$x=\frac{\sqrt{246}+16}{5}$$

Nā, me whakaoti te whārite x=\frac{32±2\sqrt{246}}{10} ina he tango te ±. Tango 2\sqrt{246} mai i 32.

$$x=\frac{32-2\sqrt{246}}{10}$$

Whakawehe 32-2\sqrt{246} ki te 10.

$$x=\frac{16-\sqrt{246}}{5}$$

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{16+\sqrt{246}}{5} mō te x_{1} me te \frac{16-\sqrt{246}}{5} mō te x_{2}.

$$5x^{2}-32x+2=5\left(x-\frac{\sqrt{246}+16}{5}\right)\left(x-\frac{16-\sqrt{246}}{5}\right)$$

Aromātai

$$5x^{2}-32x+2$$