Whakaoti i te {l}{2x^2+4x}{-12}

$$\left. \begin{array} { l } { 2 x ^ { 2 } + 4 x } \\ { - 12 } \end{array} \right.$$

Tauwehe

$$2\left(x-\left(-\sqrt{7}-1\right)\right)\left(x-\left(\sqrt{7}-1\right)\right)$$

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.

$$2x^{2}+4x-12=0$$

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.

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

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\times 2\left(-12\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-4±\sqrt{16-8\left(-12\right)}}{2\times 2}$$

Whakareatia -8 ki te -12.

$$x=\frac{-4±\sqrt{16+96}}{2\times 2}$$

Tāpiri 16 ki te 96.

$$x=\frac{-4±\sqrt{112}}{2\times 2}$$

Tuhia te pūtakerua o te 112.

$$x=\frac{-4±4\sqrt{7}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-4±4\sqrt{7}}{4}$$

Nā, me whakaoti te whārite x=\frac{-4±4\sqrt{7}}{4} ina he tāpiri te ±. Tāpiri -4 ki te 4\sqrt{7}.

$$x=\frac{4\sqrt{7}-4}{4}$$

Whakawehe -4+4\sqrt{7} ki te 4.

$$x=\sqrt{7}-1$$

Nā, me whakaoti te whārite x=\frac{-4±4\sqrt{7}}{4} ina he tango te ±. Tango 4\sqrt{7} mai i -4.

$$x=\frac{-4\sqrt{7}-4}{4}$$

Whakawehe -4-4\sqrt{7} ki te 4.

$$x=-\sqrt{7}-1$$

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 -1+\sqrt{7} mō te x_{1} me te -1-\sqrt{7} mō te x_{2}.

$$2x^{2}+4x-12=2\left(x-\left(\sqrt{7}-1\right)\right)\left(x-\left(-\sqrt{7}-1\right)\right)$$

Aromātai

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