Whakaoti i te 2m-14quaddiv1/m^2-3m-28

$$2 m - 14 \quad \div \frac { 1 } { m ^ { 2 } - 3 m - 28 }$$

Aromātai

$$392+44m-14m^{2}$$

Ngā Upane Otinga

Whakawehe 14 ki te \frac{1}{m^{2}-3m-28} mā te whakarea 14 ki te tau huripoki o \frac{1}{m^{2}-3m-28}.

$$2m-14\left(m^{2}-3m-28\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 14 ki te m^{2}-3m-28.

$$2m-\left(14m^{2}-42m-392\right)$$

Hei kimi i te tauaro o 14m^{2}-42m-392, kimihia te tauaro o ia taurangi.

$$2m-14m^{2}+42m+392$$

Pahekotia te 2m me 42m, ka 44m.

$$44m-14m^{2}+392$$

Tauwehe

$$-14\left(m-\frac{11-\sqrt{1493}}{7}\right)\left(m-\frac{\sqrt{1493}+11}{7}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehe 14 ki te \frac{1}{m^{2}-3m-28} mā te whakarea 14 ki te tau huripoki o \frac{1}{m^{2}-3m-28}.

$$factor(2m-14\left(m^{2}-3m-28\right))$$

Whakamahia te āhuatanga tohatoha hei whakarea te 14 ki te m^{2}-3m-28.

$$factor(2m-\left(14m^{2}-42m-392\right))$$

Hei kimi i te tauaro o 14m^{2}-42m-392, kimihia te tauaro o ia taurangi.

$$factor(2m-14m^{2}+42m+392)$$

Pahekotia te 2m me 42m, ka 44m.

$$factor(44m-14m^{2}+392)$$

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.

$$-14m^{2}+44m+392=0$$

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.

$$m=\frac{-44±\sqrt{44^{2}-4\left(-14\right)\times 392}}{2\left(-14\right)}$$

Pūrua 44.

$$m=\frac{-44±\sqrt{1936-4\left(-14\right)\times 392}}{2\left(-14\right)}$$

Whakareatia -4 ki te -14.

$$m=\frac{-44±\sqrt{1936+56\times 392}}{2\left(-14\right)}$$

Whakareatia 56 ki te 392.

$$m=\frac{-44±\sqrt{1936+21952}}{2\left(-14\right)}$$

Tāpiri 1936 ki te 21952.

$$m=\frac{-44±\sqrt{23888}}{2\left(-14\right)}$$

Tuhia te pūtakerua o te 23888.

$$m=\frac{-44±4\sqrt{1493}}{2\left(-14\right)}$$

Whakareatia 2 ki te -14.

$$m=\frac{-44±4\sqrt{1493}}{-28}$$

Nā, me whakaoti te whārite m=\frac{-44±4\sqrt{1493}}{-28} ina he tāpiri te ±. Tāpiri -44 ki te 4\sqrt{1493}.

$$m=\frac{4\sqrt{1493}-44}{-28}$$

Whakawehe -44+4\sqrt{1493} ki te -28.

$$m=\frac{11-\sqrt{1493}}{7}$$

Nā, me whakaoti te whārite m=\frac{-44±4\sqrt{1493}}{-28} ina he tango te ±. Tango 4\sqrt{1493} mai i -44.

$$m=\frac{-4\sqrt{1493}-44}{-28}$$

Whakawehe -44-4\sqrt{1493} ki te -28.

$$m=\frac{\sqrt{1493}+11}{7}$$

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{11-\sqrt{1493}}{7} mō te x_{1} me te \frac{11+\sqrt{1493}}{7} mō te x_{2}.

$$-14m^{2}+44m+392=-14\left(m-\frac{11-\sqrt{1493}}{7}\right)\left(m-\frac{\sqrt{1493}+11}{7}\right)$$