Whakaoti i te m-61m^2-11m+30

$$m - 61 m ^ { 2 } - 11 m + 30$$

Tauwehe

$$-61\left(m-\frac{-\sqrt{1855}-5}{61}\right)\left(m-\frac{\sqrt{1855}-5}{61}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te m me -11m, ka -10m.

$$factor(-10m-61m^{2}+30)$$

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.

$$-61m^{2}-10m+30=0$$

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.

$$m=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-61\right)\times 30}}{2\left(-61\right)}$$

Pūrua -10.

$$m=\frac{-\left(-10\right)±\sqrt{100-4\left(-61\right)\times 30}}{2\left(-61\right)}$$

Whakareatia -4 ki te -61.

$$m=\frac{-\left(-10\right)±\sqrt{100+244\times 30}}{2\left(-61\right)}$$

Whakareatia 244 ki te 30.

$$m=\frac{-\left(-10\right)±\sqrt{100+7320}}{2\left(-61\right)}$$

Tāpiri 100 ki te 7320.

$$m=\frac{-\left(-10\right)±\sqrt{7420}}{2\left(-61\right)}$$

Tuhia te pūtakerua o te 7420.

$$m=\frac{-\left(-10\right)±2\sqrt{1855}}{2\left(-61\right)}$$

Ko te tauaro o -10 ko 10.

$$m=\frac{10±2\sqrt{1855}}{2\left(-61\right)}$$

Whakareatia 2 ki te -61.

$$m=\frac{10±2\sqrt{1855}}{-122}$$

Nā, me whakaoti te whārite m=\frac{10±2\sqrt{1855}}{-122} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{1855}.

$$m=\frac{2\sqrt{1855}+10}{-122}$$

Whakawehe 10+2\sqrt{1855} ki te -122.

$$m=\frac{-\sqrt{1855}-5}{61}$$

Nā, me whakaoti te whārite m=\frac{10±2\sqrt{1855}}{-122} ina he tango te ±. Tango 2\sqrt{1855} mai i 10.

$$m=\frac{10-2\sqrt{1855}}{-122}$$

Whakawehe 10-2\sqrt{1855} ki te -122.

$$m=\frac{\sqrt{1855}-5}{61}$$

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{-5-\sqrt{1855}}{61} mō te x_{1} me te \frac{-5+\sqrt{1855}}{61} mō te x_{2}.

$$-61m^{2}-10m+30=-61\left(m-\frac{-\sqrt{1855}-5}{61}\right)\left(m-\frac{\sqrt{1855}-5}{61}\right)$$

Aromātai

$$30-10m-61m^{2}$$

Ngā Upane Otinga

Pahekotia te m me -11m, ka -10m.

$$-10m-61m^{2}+30$$