Whakaoti i te 150x^2-180x-57

$$150 x ^ { 2 } - 180 x - 57$$

Tauwehe

$$150\left(x-\left(-\frac{\sqrt{74}}{10}+\frac{3}{5}\right)\right)\left(x-\left(\frac{\sqrt{74}}{10}+\frac{3}{5}\right)\right)$$

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.

$$150x^{2}-180x-57=0$$

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.

$$x=\frac{-\left(-180\right)±\sqrt{\left(-180\right)^{2}-4\times 150\left(-57\right)}}{2\times 150}$$

Pūrua -180.

$$x=\frac{-\left(-180\right)±\sqrt{32400-4\times 150\left(-57\right)}}{2\times 150}$$

Whakareatia -4 ki te 150.

$$x=\frac{-\left(-180\right)±\sqrt{32400-600\left(-57\right)}}{2\times 150}$$

Whakareatia -600 ki te -57.

$$x=\frac{-\left(-180\right)±\sqrt{32400+34200}}{2\times 150}$$

Tāpiri 32400 ki te 34200.

$$x=\frac{-\left(-180\right)±\sqrt{66600}}{2\times 150}$$

Tuhia te pūtakerua o te 66600.

$$x=\frac{-\left(-180\right)±30\sqrt{74}}{2\times 150}$$

Ko te tauaro o -180 ko 180.

$$x=\frac{180±30\sqrt{74}}{2\times 150}$$

Whakareatia 2 ki te 150.

$$x=\frac{180±30\sqrt{74}}{300}$$

Nā, me whakaoti te whārite x=\frac{180±30\sqrt{74}}{300} ina he tāpiri te ±. Tāpiri 180 ki te 30\sqrt{74}.

$$x=\frac{30\sqrt{74}+180}{300}$$

Whakawehe 180+30\sqrt{74} ki te 300.

$$x=\frac{\sqrt{74}}{10}+\frac{3}{5}$$

Nā, me whakaoti te whārite x=\frac{180±30\sqrt{74}}{300} ina he tango te ±. Tango 30\sqrt{74} mai i 180.

$$x=\frac{180-30\sqrt{74}}{300}$$

Whakawehe 180-30\sqrt{74} ki te 300.

$$x=-\frac{\sqrt{74}}{10}+\frac{3}{5}$$

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{3}{5}+\frac{\sqrt{74}}{10} mō te x_{1} me te \frac{3}{5}-\frac{\sqrt{74}}{10} mō te x_{2}.

$$150x^{2}-180x-57=150\left(x-\left(\frac{\sqrt{74}}{10}+\frac{3}{5}\right)\right)\left(x-\left(-\frac{\sqrt{74}}{10}+\frac{3}{5}\right)\right)$$

Aromātai

$$150x^{2}-180x-57$$