Whakaoti i te -4x^2+16x-2

$$- 4 x ^ { 2 } + 16 x - 2$$

Tauwehe

$$-4\left(x-\left(-\frac{\sqrt{14}}{2}+2\right)\right)\left(x-\left(\frac{\sqrt{14}}{2}+2\right)\right)$$

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.

$$-4x^{2}+16x-2=0$$

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.

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

Pūrua 16.

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

Whakareatia -4 ki te -4.

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

Whakareatia 16 ki te -2.

$$x=\frac{-16±\sqrt{256-32}}{2\left(-4\right)}$$

Tāpiri 256 ki te -32.

$$x=\frac{-16±\sqrt{224}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 224.

$$x=\frac{-16±4\sqrt{14}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-16±4\sqrt{14}}{-8}$$

Nā, me whakaoti te whārite x=\frac{-16±4\sqrt{14}}{-8} ina he tāpiri te ±. Tāpiri -16 ki te 4\sqrt{14}.

$$x=\frac{4\sqrt{14}-16}{-8}$$

Whakawehe -16+4\sqrt{14} ki te -8.

$$x=-\frac{\sqrt{14}}{2}+2$$

Nā, me whakaoti te whārite x=\frac{-16±4\sqrt{14}}{-8} ina he tango te ±. Tango 4\sqrt{14} mai i -16.

$$x=\frac{-4\sqrt{14}-16}{-8}$$

Whakawehe -16-4\sqrt{14} ki te -8.

$$x=\frac{\sqrt{14}}{2}+2$$

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 2-\frac{\sqrt{14}}{2} mō te x_{1} me te 2+\frac{\sqrt{14}}{2} mō te x_{2}.

$$-4x^{2}+16x-2=-4\left(x-\left(-\frac{\sqrt{14}}{2}+2\right)\right)\left(x-\left(\frac{\sqrt{14}}{2}+2\right)\right)$$

Aromātai

$$-4x^{2}+16x-2$$