Whakaoti i te x^2-2x-80

$$x ^ { 2 } - 2 x - 80$$

Tauwehe

$$\left(x-10\right)\left(x+8\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-80. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=1\left(-80\right)=-80$$

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 -80.

$$1,-80 2,-40 4,-20 5,-16 8,-10$$

Tātaihia te tapeke mō ia takirua.

$$1-80=-79 2-40=-38 4-20=-16 5-16=-11 8-10=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-10 b=8$$

Tuhia anō te x^{2}-2x-80 hei \left(x^{2}-10x\right)+\left(8x-80\right).

$$\left(x^{2}-10x\right)+\left(8x-80\right)$$

Tauwehea te x i te tuatahi me te 8 i te rōpū tuarua.

$$x\left(x-10\right)+8\left(x-10\right)$$

Whakatauwehea atu te kīanga pātahi x-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-10\right)\left(x+8\right)$$

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.

$$x^{2}-2x-80=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-80\right)}}{2}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-80\right)}}{2}$$

Whakareatia -4 ki te -80.

$$x=\frac{-\left(-2\right)±\sqrt{4+320}}{2}$$

Tāpiri 4 ki te 320.

$$x=\frac{-\left(-2\right)±\sqrt{324}}{2}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{-\left(-2\right)±18}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±18}{2}$$

Nā, me whakaoti te whārite x=\frac{2±18}{2} ina he tāpiri te ±. Tāpiri 2 ki te 18.

$$x=\frac{20}{2}$$

Whakawehe 20 ki te 2.

$$x=10$$

Nā, me whakaoti te whārite x=\frac{2±18}{2} ina he tango te ±. Tango 18 mai i 2.

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

Whakawehe -16 ki te 2.

$$x=-8$$

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 10 mō te x_{1} me te -8 mō te x_{2}.

$$x^{2}-2x-80=\left(x-10\right)\left(x-\left(-8\right)\right)$$

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

$$x^{2}-2x-80=\left(x-10\right)\left(x+8\right)$$

Aromātai

$$\left(x-10\right)\left(x+8\right)$$