Whakaoti i te -x^2+25x+15

$$- { x }^{ 2 } +25x+15$$

Tauwehe

$$-\left(x-\frac{25-\sqrt{685}}{2}\right)\left(x-\frac{\sqrt{685}+25}{2}\right)$$

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.

$$-x^{2}+25x+15=0$$

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.

$$x=\frac{-25±\sqrt{25^{2}-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Pūrua 25.

$$x=\frac{-25±\sqrt{625-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-25±\sqrt{625+4\times 15}}{2\left(-1\right)}$$

Whakareatia 4 ki te 15.

$$x=\frac{-25±\sqrt{625+60}}{2\left(-1\right)}$$

Tāpiri 625 ki te 60.

$$x=\frac{-25±\sqrt{685}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-25±\sqrt{685}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-25±\sqrt{685}}{-2} ina he tāpiri te ±. Tāpiri -25 ki te \sqrt{685}.

$$x=\frac{\sqrt{685}-25}{-2}$$

Whakawehe -25+\sqrt{685} ki te -2.

$$x=\frac{25-\sqrt{685}}{2}$$

Nā, me whakaoti te whārite x=\frac{-25±\sqrt{685}}{-2} ina he tango te ±. Tango \sqrt{685} mai i -25.

$$x=\frac{-\sqrt{685}-25}{-2}$$

Whakawehe -25-\sqrt{685} ki te -2.

$$x=\frac{\sqrt{685}+25}{2}$$

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 \frac{25-\sqrt{685}}{2} mō te x_{1} me te \frac{25+\sqrt{685}}{2} mō te x_{2}.

$$-x^{2}+25x+15=-\left(x-\frac{25-\sqrt{685}}{2}\right)\left(x-\frac{\sqrt{685}+25}{2}\right)$$

Aromātai

$$15+25x-x^{2}$$