Whakaoti i te x^2-489x+28680

$${ x }^{ 2 } -489x+28680$$

Tauwehe

$$\left(x-\frac{489-\sqrt{124401}}{2}\right)\left(x-\frac{\sqrt{124401}+489}{2}\right)$$

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.

$$x^{2}-489x+28680=0$$

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.

$$x=\frac{-\left(-489\right)±\sqrt{\left(-489\right)^{2}-4\times 28680}}{2}$$

Pūrua -489.

$$x=\frac{-\left(-489\right)±\sqrt{239121-4\times 28680}}{2}$$

Whakareatia -4 ki te 28680.

$$x=\frac{-\left(-489\right)±\sqrt{239121-114720}}{2}$$

Tāpiri 239121 ki te -114720.

$$x=\frac{-\left(-489\right)±\sqrt{124401}}{2}$$

Ko te tauaro o -489 ko 489.

$$x=\frac{489±\sqrt{124401}}{2}$$

Nā, me whakaoti te whārite x=\frac{489±\sqrt{124401}}{2} ina he tāpiri te ±. Tāpiri 489 ki te \sqrt{124401}.

$$x=\frac{\sqrt{124401}+489}{2}$$

Nā, me whakaoti te whārite x=\frac{489±\sqrt{124401}}{2} ina he tango te ±. Tango \sqrt{124401} mai i 489.

$$x=\frac{489-\sqrt{124401}}{2}$$

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{489+\sqrt{124401}}{2} mō te x_{1} me te \frac{489-\sqrt{124401}}{2} mō te x_{2}.

$$x^{2}-489x+28680=\left(x-\frac{\sqrt{124401}+489}{2}\right)\left(x-\frac{489-\sqrt{124401}}{2}\right)$$

Aromātai

$$x^{2}-489x+28680$$