Whakaoti i te 2x^2+18x-25

$$2 x ^ { 2 } + 18 x - 25$$

Tauwehe

$$2\left(x-\frac{-\sqrt{131}-9}{2}\right)\left(x-\frac{\sqrt{131}-9}{2}\right)$$

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.

$$2x^{2}+18x-25=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\times 2\left(-25\right)}}{2\times 2}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\times 2\left(-25\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-18±\sqrt{324-8\left(-25\right)}}{2\times 2}$$

Whakareatia -8 ki te -25.

$$x=\frac{-18±\sqrt{324+200}}{2\times 2}$$

Tāpiri 324 ki te 200.

$$x=\frac{-18±\sqrt{524}}{2\times 2}$$

Tuhia te pūtakerua o te 524.

$$x=\frac{-18±2\sqrt{131}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-18±2\sqrt{131}}{4}$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{131}}{4} ina he tāpiri te ±. Tāpiri -18 ki te 2\sqrt{131}.

$$x=\frac{2\sqrt{131}-18}{4}$$

Whakawehe -18+2\sqrt{131} ki te 4.

$$x=\frac{\sqrt{131}-9}{2}$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{131}}{4} ina he tango te ±. Tango 2\sqrt{131} mai i -18.

$$x=\frac{-2\sqrt{131}-18}{4}$$

Whakawehe -18-2\sqrt{131} ki te 4.

$$x=\frac{-\sqrt{131}-9}{2}$$

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{-9+\sqrt{131}}{2} mō te x_{1} me te \frac{-9-\sqrt{131}}{2} mō te x_{2}.

$$2x^{2}+18x-25=2\left(x-\frac{\sqrt{131}-9}{2}\right)\left(x-\frac{-\sqrt{131}-9}{2}\right)$$

Aromātai

$$2x^{2}+18x-25$$