Whakaoti i te 60x^2-30x-200

$$60 { x }^{ 2 } -30x-200$$

Tauwehe

$$60\left(x-\left(-\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)\left(x-\left(\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)$$

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.

$$60x^{2}-30x-200=0$$

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.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}-4\times 60\left(-200\right)}}{2\times 60}$$

Pūrua -30.

$$x=\frac{-\left(-30\right)±\sqrt{900-4\times 60\left(-200\right)}}{2\times 60}$$

Whakareatia -4 ki te 60.

$$x=\frac{-\left(-30\right)±\sqrt{900-240\left(-200\right)}}{2\times 60}$$

Whakareatia -240 ki te -200.

$$x=\frac{-\left(-30\right)±\sqrt{900+48000}}{2\times 60}$$

Tāpiri 900 ki te 48000.

$$x=\frac{-\left(-30\right)±\sqrt{48900}}{2\times 60}$$

Tuhia te pūtakerua o te 48900.

$$x=\frac{-\left(-30\right)±10\sqrt{489}}{2\times 60}$$

Ko te tauaro o -30 ko 30.

$$x=\frac{30±10\sqrt{489}}{2\times 60}$$

Whakareatia 2 ki te 60.

$$x=\frac{30±10\sqrt{489}}{120}$$

Nā, me whakaoti te whārite x=\frac{30±10\sqrt{489}}{120} ina he tāpiri te ±. Tāpiri 30 ki te 10\sqrt{489}.

$$x=\frac{10\sqrt{489}+30}{120}$$

Whakawehe 30+10\sqrt{489} ki te 120.

$$x=\frac{\sqrt{489}}{12}+\frac{1}{4}$$

Nā, me whakaoti te whārite x=\frac{30±10\sqrt{489}}{120} ina he tango te ±. Tango 10\sqrt{489} mai i 30.

$$x=\frac{30-10\sqrt{489}}{120}$$

Whakawehe 30-10\sqrt{489} ki te 120.

$$x=-\frac{\sqrt{489}}{12}+\frac{1}{4}$$

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{1}{4}+\frac{\sqrt{489}}{12} mō te x_{1} me te \frac{1}{4}-\frac{\sqrt{489}}{12} mō te x_{2}.

$$60x^{2}-30x-200=60\left(x-\left(\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)\left(x-\left(-\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)$$

Aromātai

$$60x^{2}-30x-200$$