Whakaoti i te 2x^2+16x-1

$$2 x ^ { 2 } + 16 x - 1$$

Tauwehe

$$2\left(x-\left(-\frac{\sqrt{66}}{2}-4\right)\right)\left(x-\left(\frac{\sqrt{66}}{2}-4\right)\right)$$

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.

$$2x^{2}+16x-1=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\times 2\left(-1\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-16±\sqrt{256-8\left(-1\right)}}{2\times 2}$$

Whakareatia -8 ki te -1.

$$x=\frac{-16±\sqrt{256+8}}{2\times 2}$$

Tāpiri 256 ki te 8.

$$x=\frac{-16±\sqrt{264}}{2\times 2}$$

Tuhia te pūtakerua o te 264.

$$x=\frac{-16±2\sqrt{66}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-16±2\sqrt{66}}{4}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{66}}{4} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{66}.

$$x=\frac{2\sqrt{66}-16}{4}$$

Whakawehe -16+2\sqrt{66} ki te 4.

$$x=\frac{\sqrt{66}}{2}-4$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{66}}{4} ina he tango te ±. Tango 2\sqrt{66} mai i -16.

$$x=\frac{-2\sqrt{66}-16}{4}$$

Whakawehe -16-2\sqrt{66} ki te 4.

$$x=-\frac{\sqrt{66}}{2}-4$$

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 -4+\frac{\sqrt{66}}{2} mō te x_{1} me te -4-\frac{\sqrt{66}}{2} mō te x_{2}.

$$2x^{2}+16x-1=2\left(x-\left(\frac{\sqrt{66}}{2}-4\right)\right)\left(x-\left(-\frac{\sqrt{66}}{2}-4\right)\right)$$

Aromātai

$$2x^{2}+16x-1$$