Whakaoti i te 7m^2+7m-504

$$7 m ^ { 2 } + 7 m - 504$$

Tauwehe

$$7\left(m-8\right)\left(m+9\right)$$

Ngā Upane Otinga

Tauwehea te 7.

$$7\left(m^{2}+m-72\right)$$

Whakaarohia te m^{2}+m-72. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm-72. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-72\right)=-72$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -72.

$$-1,72 -2,36 -3,24 -4,18 -6,12 -8,9$$

Tātaihia te tapeke mō ia takirua.

$$-1+72=71 -2+36=34 -3+24=21 -4+18=14 -6+12=6 -8+9=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-8 b=9$$

Tuhia anō te m^{2}+m-72 hei \left(m^{2}-8m\right)+\left(9m-72\right).

$$\left(m^{2}-8m\right)+\left(9m-72\right)$$

Tauwehea te m i te tuatahi me te 9 i te rōpū tuarua.

$$m\left(m-8\right)+9\left(m-8\right)$$

Whakatauwehea atu te kīanga pātahi m-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-8\right)\left(m+9\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$7\left(m-8\right)\left(m+9\right)$$

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.

$$7m^{2}+7m-504=0$$

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.

$$m=\frac{-7±\sqrt{7^{2}-4\times 7\left(-504\right)}}{2\times 7}$$

Pūrua 7.

$$m=\frac{-7±\sqrt{49-4\times 7\left(-504\right)}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$m=\frac{-7±\sqrt{49-28\left(-504\right)}}{2\times 7}$$

Whakareatia -28 ki te -504.

$$m=\frac{-7±\sqrt{49+14112}}{2\times 7}$$

Tāpiri 49 ki te 14112.

$$m=\frac{-7±\sqrt{14161}}{2\times 7}$$

Tuhia te pūtakerua o te 14161.

$$m=\frac{-7±119}{2\times 7}$$

Whakareatia 2 ki te 7.

$$m=\frac{-7±119}{14}$$

Nā, me whakaoti te whārite m=\frac{-7±119}{14} ina he tāpiri te ±. Tāpiri -7 ki te 119.

$$m=\frac{112}{14}$$

Whakawehe 112 ki te 14.

$$m=8$$

Nā, me whakaoti te whārite m=\frac{-7±119}{14} ina he tango te ±. Tango 119 mai i -7.

$$m=-\frac{126}{14}$$

Whakawehe -126 ki te 14.

$$m=-9$$

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 8 mō te x_{1} me te -9 mō te x_{2}.

$$7m^{2}+7m-504=7\left(m-8\right)\left(m-\left(-9\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$7m^{2}+7m-504=7\left(m-8\right)\left(m+9\right)$$

Aromātai

$$7\left(m-8\right)\left(m+9\right)$$