Whakaoti i te -2x^2+17x+39

$$-2 { x }^{ 2 } +17x+39$$

Tauwehe

$$-2\left(x-\frac{17-\sqrt{601}}{4}\right)\left(x-\frac{\sqrt{601}+17}{4}\right)$$

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.

$$-2x^{2}+17x+39=0$$

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.

$$x=\frac{-17±\sqrt{17^{2}-4\left(-2\right)\times 39}}{2\left(-2\right)}$$

Pūrua 17.

$$x=\frac{-17±\sqrt{289-4\left(-2\right)\times 39}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-17±\sqrt{289+8\times 39}}{2\left(-2\right)}$$

Whakareatia 8 ki te 39.

$$x=\frac{-17±\sqrt{289+312}}{2\left(-2\right)}$$

Tāpiri 289 ki te 312.

$$x=\frac{-17±\sqrt{601}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-17±\sqrt{601}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{601}}{-4} ina he tāpiri te ±. Tāpiri -17 ki te \sqrt{601}.

$$x=\frac{\sqrt{601}-17}{-4}$$

Whakawehe -17+\sqrt{601} ki te -4.

$$x=\frac{17-\sqrt{601}}{4}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{601}}{-4} ina he tango te ±. Tango \sqrt{601} mai i -17.

$$x=\frac{-\sqrt{601}-17}{-4}$$

Whakawehe -17-\sqrt{601} ki te -4.

$$x=\frac{\sqrt{601}+17}{4}$$

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 \frac{17-\sqrt{601}}{4} mō te x_{1} me te \frac{17+\sqrt{601}}{4} mō te x_{2}.

$$-2x^{2}+17x+39=-2\left(x-\frac{17-\sqrt{601}}{4}\right)\left(x-\frac{\sqrt{601}+17}{4}\right)$$

Aromātai

$$39+17x-2x^{2}$$