Whakaoti i te -5x^2+16x+20

$$- 5 x ^ { 2 } + 16 x + 20$$

Tauwehe

$$-5\left(x-\frac{8-2\sqrt{41}}{5}\right)\left(x-\frac{2\sqrt{41}+8}{5}\right)$$

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.

$$-5x^{2}+16x+20=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-5\right)\times 20}}{2\left(-5\right)}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-5\right)\times 20}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$x=\frac{-16±\sqrt{256+20\times 20}}{2\left(-5\right)}$$

Whakareatia 20 ki te 20.

$$x=\frac{-16±\sqrt{256+400}}{2\left(-5\right)}$$

Tāpiri 256 ki te 400.

$$x=\frac{-16±\sqrt{656}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 656.

$$x=\frac{-16±4\sqrt{41}}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=\frac{-16±4\sqrt{41}}{-10}$$

Nā, me whakaoti te whārite x=\frac{-16±4\sqrt{41}}{-10} ina he tāpiri te ±. Tāpiri -16 ki te 4\sqrt{41}.

$$x=\frac{4\sqrt{41}-16}{-10}$$

Whakawehe -16+4\sqrt{41} ki te -10.

$$x=\frac{8-2\sqrt{41}}{5}$$

Nā, me whakaoti te whārite x=\frac{-16±4\sqrt{41}}{-10} ina he tango te ±. Tango 4\sqrt{41} mai i -16.

$$x=\frac{-4\sqrt{41}-16}{-10}$$

Whakawehe -16-4\sqrt{41} ki te -10.

$$x=\frac{2\sqrt{41}+8}{5}$$

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{8-2\sqrt{41}}{5} mō te x_{1} me te \frac{8+2\sqrt{41}}{5} mō te x_{2}.

$$-5x^{2}+16x+20=-5\left(x-\frac{8-2\sqrt{41}}{5}\right)\left(x-\frac{2\sqrt{41}+8}{5}\right)$$

Aromātai

$$20+16x-5x^{2}$$