Whakaoti i te 2x^2+12x-8

$$2 x ^ { 2 } + 12 x - 8$$

Tauwehe

$$2\left(x-\left(-\sqrt{13}-3\right)\right)\left(x-\left(\sqrt{13}-3\right)\right)$$

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.

$$2x^{2}+12x-8=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 2\left(-8\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

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

Whakareatia -8 ki te -8.

$$x=\frac{-12±\sqrt{144+64}}{2\times 2}$$

Tāpiri 144 ki te 64.

$$x=\frac{-12±\sqrt{208}}{2\times 2}$$

Tuhia te pūtakerua o te 208.

$$x=\frac{-12±4\sqrt{13}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-12±4\sqrt{13}}{4}$$

Nā, me whakaoti te whārite x=\frac{-12±4\sqrt{13}}{4} ina he tāpiri te ±. Tāpiri -12 ki te 4\sqrt{13}.

$$x=\frac{4\sqrt{13}-12}{4}$$

Whakawehe -12+4\sqrt{13} ki te 4.

$$x=\sqrt{13}-3$$

Nā, me whakaoti te whārite x=\frac{-12±4\sqrt{13}}{4} ina he tango te ±. Tango 4\sqrt{13} mai i -12.

$$x=\frac{-4\sqrt{13}-12}{4}$$

Whakawehe -12-4\sqrt{13} ki te 4.

$$x=-\sqrt{13}-3$$

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+\sqrt{13} mō te x_{1} me te -3-\sqrt{13} mō te x_{2}.

$$2x^{2}+12x-8=2\left(x-\left(\sqrt{13}-3\right)\right)\left(x-\left(-\sqrt{13}-3\right)\right)$$

Aromātai

$$2\left(x^{2}+6x-4\right)$$