Whakaoti i te -2a^2-2a+6

$$-2 { a }^{ 2 } -2a+6$$

Tauwehe

$$-2\left(a-\frac{-\sqrt{13}-1}{2}\right)\left(a-\frac{\sqrt{13}-1}{2}\right)$$

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.

$$-2a^{2}-2a+6=0$$

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.

$$a=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

Pūrua -2.

$$a=\frac{-\left(-2\right)±\sqrt{4-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$a=\frac{-\left(-2\right)±\sqrt{4+8\times 6}}{2\left(-2\right)}$$

Whakareatia 8 ki te 6.

$$a=\frac{-\left(-2\right)±\sqrt{4+48}}{2\left(-2\right)}$$

Tāpiri 4 ki te 48.

$$a=\frac{-\left(-2\right)±\sqrt{52}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 52.

$$a=\frac{-\left(-2\right)±2\sqrt{13}}{2\left(-2\right)}$$

Ko te tauaro o -2 ko 2.

$$a=\frac{2±2\sqrt{13}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$a=\frac{2±2\sqrt{13}}{-4}$$

Nā, me whakaoti te whārite a=\frac{2±2\sqrt{13}}{-4} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{13}.

$$a=\frac{2\sqrt{13}+2}{-4}$$

Whakawehe 2+2\sqrt{13} ki te -4.

$$a=\frac{-\sqrt{13}-1}{2}$$

Nā, me whakaoti te whārite a=\frac{2±2\sqrt{13}}{-4} ina he tango te ±. Tango 2\sqrt{13} mai i 2.

$$a=\frac{2-2\sqrt{13}}{-4}$$

Whakawehe 2-2\sqrt{13} ki te -4.

$$a=\frac{\sqrt{13}-1}{2}$$

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 \frac{-1-\sqrt{13}}{2} mō te x_{1} me te \frac{-1+\sqrt{13}}{2} mō te x_{2}.

$$-2a^{2}-2a+6=-2\left(a-\frac{-\sqrt{13}-1}{2}\right)\left(a-\frac{\sqrt{13}-1}{2}\right)$$

Aromātai

$$6-2a-2a^{2}$$