Whakaoti i te x^2+(-7x)+(-8)

$$x ^ { 2 } + ( - 7 x ) + ( - 8 )$$

Tauwehe

$$\left(x-8\right)\left(x+1\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=1\left(-8\right)=-8$$

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 -8.

$$1,-8 2,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-8=-7 2-4=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$a=-8 b=1$$

Tuhia anō te x^{2}-7x-8 hei \left(x^{2}-8x\right)+\left(x-8\right).

$$\left(x^{2}-8x\right)+\left(x-8\right)$$

Whakatauwehea atu x i te x^{2}-8x.

$$x\left(x-8\right)+x-8$$

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

$$\left(x-8\right)\left(x+1\right)$$

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.

$$x^{2}-7x-8=0$$

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.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\left(-8\right)}}{2}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\left(-8\right)}}{2}$$

Whakareatia -4 ki te -8.

$$x=\frac{-\left(-7\right)±\sqrt{49+32}}{2}$$

Tāpiri 49 ki te 32.

$$x=\frac{-\left(-7\right)±\sqrt{81}}{2}$$

Tuhia te pūtakerua o te 81.

$$x=\frac{-\left(-7\right)±9}{2}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±9}{2}$$

Nā, me whakaoti te whārite x=\frac{7±9}{2} ina he tāpiri te ±. Tāpiri 7 ki te 9.

$$x=\frac{16}{2}$$

Whakawehe 16 ki te 2.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{7±9}{2} ina he tango te ±. Tango 9 mai i 7.

$$x=-\frac{2}{2}$$

Whakawehe -2 ki te 2.

$$x=-1$$

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 8 mō te x_{1} me te -1 mō te x_{2}.

$$x^{2}-7x-8=\left(x-8\right)\left(x-\left(-1\right)\right)$$

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

$$x^{2}-7x-8=\left(x-8\right)\left(x+1\right)$$

Aromātai

$$\left(x-8\right)\left(x+1\right)$$