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

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

Tauwehe

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

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.

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

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.

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

Pūrua -4.

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

Whakareatia -4 ki te -2.

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

Whakareatia 8 ki te 2.

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

Tāpiri 16 ki te 16.

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

Tuhia te pūtakerua o te 32.

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

Ko te tauaro o -4 ko 4.

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

Whakareatia 2 ki te -2.

$$x=\frac{4±4\sqrt{2}}{-4}$$

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

$$x=\frac{4\sqrt{2}+4}{-4}$$

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

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

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

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

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

$$x=\sqrt{2}-1$$

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 -\left(1+\sqrt{2}\right) mō te x_{1} me te -1+\sqrt{2} mō te x_{2}.

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

Aromātai

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