Whakaoti i te x^2-150x+594

$$x ^ { 2 } - 150 x + 594$$

Tauwehe

$$\left(x-\left(75-3\sqrt{559}\right)\right)\left(x-\left(3\sqrt{559}+75\right)\right)$$

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.

$$x^{2}-150x+594=0$$

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.

$$x=\frac{-\left(-150\right)±\sqrt{\left(-150\right)^{2}-4\times 594}}{2}$$

Pūrua -150.

$$x=\frac{-\left(-150\right)±\sqrt{22500-4\times 594}}{2}$$

Whakareatia -4 ki te 594.

$$x=\frac{-\left(-150\right)±\sqrt{22500-2376}}{2}$$

Tāpiri 22500 ki te -2376.

$$x=\frac{-\left(-150\right)±\sqrt{20124}}{2}$$

Tuhia te pūtakerua o te 20124.

$$x=\frac{-\left(-150\right)±6\sqrt{559}}{2}$$

Ko te tauaro o -150 ko 150.

$$x=\frac{150±6\sqrt{559}}{2}$$

Nā, me whakaoti te whārite x=\frac{150±6\sqrt{559}}{2} ina he tāpiri te ±. Tāpiri 150 ki te 6\sqrt{559}.

$$x=\frac{6\sqrt{559}+150}{2}$$

Whakawehe 150+6\sqrt{559} ki te 2.

$$x=3\sqrt{559}+75$$

Nā, me whakaoti te whārite x=\frac{150±6\sqrt{559}}{2} ina he tango te ±. Tango 6\sqrt{559} mai i 150.

$$x=\frac{150-6\sqrt{559}}{2}$$

Whakawehe 150-6\sqrt{559} ki te 2.

$$x=75-3\sqrt{559}$$

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 75+3\sqrt{559} mō te x_{1} me te 75-3\sqrt{559} mō te x_{2}.

$$x^{2}-150x+594=\left(x-\left(3\sqrt{559}+75\right)\right)\left(x-\left(75-3\sqrt{559}\right)\right)$$

Aromātai

$$x^{2}-150x+594$$