Whakaoti i te 2x^2-12x+13

$$2 x ^ { 2 } - 12 x + 13$$

Tauwehe

$$2\left(x-\left(-\frac{\sqrt{10}}{2}+3\right)\right)\left(x-\left(\frac{\sqrt{10}}{2}+3\right)\right)$$

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.

$$2x^{2}-12x+13=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 2\times 13}}{2\times 2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 2\times 13}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-12\right)±\sqrt{144-8\times 13}}{2\times 2}$$

Whakareatia -8 ki te 13.

$$x=\frac{-\left(-12\right)±\sqrt{144-104}}{2\times 2}$$

Tāpiri 144 ki te -104.

$$x=\frac{-\left(-12\right)±\sqrt{40}}{2\times 2}$$

Tuhia te pūtakerua o te 40.

$$x=\frac{-\left(-12\right)±2\sqrt{10}}{2\times 2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±2\sqrt{10}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{12±2\sqrt{10}}{4}$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{10}}{4} ina he tāpiri te ±. Tāpiri 12 ki te 2\sqrt{10}.

$$x=\frac{2\sqrt{10}+12}{4}$$

Whakawehe 12+2\sqrt{10} ki te 4.

$$x=\frac{\sqrt{10}}{2}+3$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{10}}{4} ina he tango te ±. Tango 2\sqrt{10} mai i 12.

$$x=\frac{12-2\sqrt{10}}{4}$$

Whakawehe 12-2\sqrt{10} ki te 4.

$$x=-\frac{\sqrt{10}}{2}+3$$

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 3+\frac{\sqrt{10}}{2} mō te x_{1} me te 3-\frac{\sqrt{10}}{2} mō te x_{2}.

$$2x^{2}-12x+13=2\left(x-\left(\frac{\sqrt{10}}{2}+3\right)\right)\left(x-\left(-\frac{\sqrt{10}}{2}+3\right)\right)$$

Aromātai

$$2x^{2}-12x+13$$