Whakaoti i te 7m^2-25m+6=

$$7 m ^ { 2 } - 25 m + 6 =$$

Tauwehe

$$7\left(m-\frac{25-\sqrt{457}}{14}\right)\left(m-\frac{\sqrt{457}+25}{14}\right)$$

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.

$$7m^{2}-25m+6=0$$

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.

$$m=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}-4\times 7\times 6}}{2\times 7}$$

Pūrua -25.

$$m=\frac{-\left(-25\right)±\sqrt{625-4\times 7\times 6}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$m=\frac{-\left(-25\right)±\sqrt{625-28\times 6}}{2\times 7}$$

Whakareatia -28 ki te 6.

$$m=\frac{-\left(-25\right)±\sqrt{625-168}}{2\times 7}$$

Tāpiri 625 ki te -168.

$$m=\frac{-\left(-25\right)±\sqrt{457}}{2\times 7}$$

Ko te tauaro o -25 ko 25.

$$m=\frac{25±\sqrt{457}}{2\times 7}$$

Whakareatia 2 ki te 7.

$$m=\frac{25±\sqrt{457}}{14}$$

Nā, me whakaoti te whārite m=\frac{25±\sqrt{457}}{14} ina he tāpiri te ±. Tāpiri 25 ki te \sqrt{457}.

$$m=\frac{\sqrt{457}+25}{14}$$

Nā, me whakaoti te whārite m=\frac{25±\sqrt{457}}{14} ina he tango te ±. Tango \sqrt{457} mai i 25.

$$m=\frac{25-\sqrt{457}}{14}$$

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{25+\sqrt{457}}{14} mō te x_{1} me te \frac{25-\sqrt{457}}{14} mō te x_{2}.

$$7m^{2}-25m+6=7\left(m-\frac{\sqrt{457}+25}{14}\right)\left(m-\frac{25-\sqrt{457}}{14}\right)$$

Aromātai

$$7m^{2}-25m+6$$