Whakaoti i te f(x)=-2x^2-36x-5

$$f ( x ) = - 2 x ^ { 2 } - 36 x - 5$$

Tauwehe

$$-2\left(x-\left(-\frac{\sqrt{314}}{2}-9\right)\right)\left(x-\left(\frac{\sqrt{314}}{2}-9\right)\right)$$

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.

$$-2x^{2}-36x-5=0$$

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.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\left(-2\right)\left(-5\right)}}{2\left(-2\right)}$$

Pūrua -36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\left(-2\right)\left(-5\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-\left(-36\right)±\sqrt{1296+8\left(-5\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -5.

$$x=\frac{-\left(-36\right)±\sqrt{1296-40}}{2\left(-2\right)}$$

Tāpiri 1296 ki te -40.

$$x=\frac{-\left(-36\right)±\sqrt{1256}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 1256.

$$x=\frac{-\left(-36\right)±2\sqrt{314}}{2\left(-2\right)}$$

Ko te tauaro o -36 ko 36.

$$x=\frac{36±2\sqrt{314}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{36±2\sqrt{314}}{-4}$$

Nā, me whakaoti te whārite x=\frac{36±2\sqrt{314}}{-4} ina he tāpiri te ±. Tāpiri 36 ki te 2\sqrt{314}.

$$x=\frac{2\sqrt{314}+36}{-4}$$

Whakawehe 36+2\sqrt{314} ki te -4.

$$x=-\frac{\sqrt{314}}{2}-9$$

Nā, me whakaoti te whārite x=\frac{36±2\sqrt{314}}{-4} ina he tango te ±. Tango 2\sqrt{314} mai i 36.

$$x=\frac{36-2\sqrt{314}}{-4}$$

Whakawehe 36-2\sqrt{314} ki te -4.

$$x=\frac{\sqrt{314}}{2}-9$$

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 -9-\frac{\sqrt{314}}{2} mō te x_{1} me te -9+\frac{\sqrt{314}}{2} mō te x_{2}.

$$-2x^{2}-36x-5=-2\left(x-\left(-\frac{\sqrt{314}}{2}-9\right)\right)\left(x-\left(\frac{\sqrt{314}}{2}-9\right)\right)$$

Aromātai

$$-2x^{2}-36x-5$$