Whakaoti i te m^2-47m+400

$$m ^ { 2 } - 47 m + 400$$

Tauwehe

$$\left(m-\frac{47-\sqrt{609}}{2}\right)\left(m-\frac{\sqrt{609}+47}{2}\right)$$

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.

$$m^{2}-47m+400=0$$

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.

$$m=\frac{-\left(-47\right)±\sqrt{\left(-47\right)^{2}-4\times 400}}{2}$$

Pūrua -47.

$$m=\frac{-\left(-47\right)±\sqrt{2209-4\times 400}}{2}$$

Whakareatia -4 ki te 400.

$$m=\frac{-\left(-47\right)±\sqrt{2209-1600}}{2}$$

Tāpiri 2209 ki te -1600.

$$m=\frac{-\left(-47\right)±\sqrt{609}}{2}$$

Ko te tauaro o -47 ko 47.

$$m=\frac{47±\sqrt{609}}{2}$$

Nā, me whakaoti te whārite m=\frac{47±\sqrt{609}}{2} ina he tāpiri te ±. Tāpiri 47 ki te \sqrt{609}.

$$m=\frac{\sqrt{609}+47}{2}$$

Nā, me whakaoti te whārite m=\frac{47±\sqrt{609}}{2} ina he tango te ±. Tango \sqrt{609} mai i 47.

$$m=\frac{47-\sqrt{609}}{2}$$

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{47+\sqrt{609}}{2} mō te x_{1} me te \frac{47-\sqrt{609}}{2} mō te x_{2}.

$$m^{2}-47m+400=\left(m-\frac{\sqrt{609}+47}{2}\right)\left(m-\frac{47-\sqrt{609}}{2}\right)$$

Aromātai

$$m^{2}-47m+400$$