Whakaoti i te f(x)=-2x^2-12x-9

$$f ( x ) = - 2 x ^ { 2 } - 12 x - 9$$

Tauwehe

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

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.

$$-2x^{2}-12x-9=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-2\right)\left(-9\right)}}{2\left(-2\right)}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-2\right)\left(-9\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-\left(-12\right)±\sqrt{144+8\left(-9\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -9.

$$x=\frac{-\left(-12\right)±\sqrt{144-72}}{2\left(-2\right)}$$

Tāpiri 144 ki te -72.

$$x=\frac{-\left(-12\right)±\sqrt{72}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 72.

$$x=\frac{-\left(-12\right)±6\sqrt{2}}{2\left(-2\right)}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±6\sqrt{2}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{12±6\sqrt{2}}{-4}$$

Nā, me whakaoti te whārite x=\frac{12±6\sqrt{2}}{-4} ina he tāpiri te ±. Tāpiri 12 ki te 6\sqrt{2}.

$$x=\frac{6\sqrt{2}+12}{-4}$$

Whakawehe 12+6\sqrt{2} ki te -4.

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

Nā, me whakaoti te whārite x=\frac{12±6\sqrt{2}}{-4} ina he tango te ±. Tango 6\sqrt{2} mai i 12.

$$x=\frac{12-6\sqrt{2}}{-4}$$

Whakawehe 12-6\sqrt{2} ki te -4.

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

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

$$-2x^{2}-12x-9=-2\left(x-\left(-\frac{3\sqrt{2}}{2}-3\right)\right)\left(x-\left(\frac{3\sqrt{2}}{2}-3\right)\right)$$

Aromātai

$$-2x^{2}-12x-9$$