Whakaoti i te -2x^2+8x+5

$$- 2 x ^ { 2 } + 8 x + 5$$

Tauwehe

$$-2\left(x-\left(-\frac{\sqrt{26}}{2}+2\right)\right)\left(x-\left(\frac{\sqrt{26}}{2}+2\right)\right)$$

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.

$$-2x^{2}+8x+5=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-2\right)\times 5}}{2\left(-2\right)}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-2\right)\times 5}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-8±\sqrt{64+8\times 5}}{2\left(-2\right)}$$

Whakareatia 8 ki te 5.

$$x=\frac{-8±\sqrt{64+40}}{2\left(-2\right)}$$

Tāpiri 64 ki te 40.

$$x=\frac{-8±\sqrt{104}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 104.

$$x=\frac{-8±2\sqrt{26}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-8±2\sqrt{26}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{26}}{-4} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{26}.

$$x=\frac{2\sqrt{26}-8}{-4}$$

Whakawehe -8+2\sqrt{26} ki te -4.

$$x=-\frac{\sqrt{26}}{2}+2$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{26}}{-4} ina he tango te ±. Tango 2\sqrt{26} mai i -8.

$$x=\frac{-2\sqrt{26}-8}{-4}$$

Whakawehe -8-2\sqrt{26} ki te -4.

$$x=\frac{\sqrt{26}}{2}+2$$

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 2-\frac{\sqrt{26}}{2} mō te x_{1} me te 2+\frac{\sqrt{26}}{2} mō te x_{2}.

$$-2x^{2}+8x+5=-2\left(x-\left(-\frac{\sqrt{26}}{2}+2\right)\right)\left(x-\left(\frac{\sqrt{26}}{2}+2\right)\right)$$

Aromātai

$$5+8x-2x^{2}$$