Whakaoti i te 6w^2-66w-72

$$6 w ^ { 2 } - 66 w - 72$$

Tauwehe

$$6\left(w-12\right)\left(w+1\right)$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(w^{2}-11w-12\right)$$

Whakaarohia te w^{2}-11w-12. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei w^{2}+aw+bw-12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=1\left(-12\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$1,-12 2,-6 3,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-12=-11 2-6=-4 3-4=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-12 b=1$$

Tuhia anō te w^{2}-11w-12 hei \left(w^{2}-12w\right)+\left(w-12\right).

$$\left(w^{2}-12w\right)+\left(w-12\right)$$

Whakatauwehea atu w i te w^{2}-12w.

$$w\left(w-12\right)+w-12$$

Whakatauwehea atu te kīanga pātahi w-12 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(w-12\right)\left(w+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6\left(w-12\right)\left(w+1\right)$$

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.

$$6w^{2}-66w-72=0$$

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.

$$w=\frac{-\left(-66\right)±\sqrt{\left(-66\right)^{2}-4\times 6\left(-72\right)}}{2\times 6}$$

Pūrua -66.

$$w=\frac{-\left(-66\right)±\sqrt{4356-4\times 6\left(-72\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$w=\frac{-\left(-66\right)±\sqrt{4356-24\left(-72\right)}}{2\times 6}$$

Whakareatia -24 ki te -72.

$$w=\frac{-\left(-66\right)±\sqrt{4356+1728}}{2\times 6}$$

Tāpiri 4356 ki te 1728.

$$w=\frac{-\left(-66\right)±\sqrt{6084}}{2\times 6}$$

Tuhia te pūtakerua o te 6084.

$$w=\frac{-\left(-66\right)±78}{2\times 6}$$

Ko te tauaro o -66 ko 66.

$$w=\frac{66±78}{2\times 6}$$

Whakareatia 2 ki te 6.

$$w=\frac{66±78}{12}$$

Nā, me whakaoti te whārite w=\frac{66±78}{12} ina he tāpiri te ±. Tāpiri 66 ki te 78.

$$w=\frac{144}{12}$$

Whakawehe 144 ki te 12.

$$w=12$$

Nā, me whakaoti te whārite w=\frac{66±78}{12} ina he tango te ±. Tango 78 mai i 66.

$$w=-\frac{12}{12}$$

Whakawehe -12 ki te 12.

$$w=-1$$

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 12 mō te x_{1} me te -1 mō te x_{2}.

$$6w^{2}-66w-72=6\left(w-12\right)\left(w-\left(-1\right)\right)$$

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

$$6w^{2}-66w-72=6\left(w-12\right)\left(w+1\right)$$

Aromātai

$$6\left(w-12\right)\left(w+1\right)$$