Whakaoti i te x^2-6x-160

$$x^2-6x-160$$

Tauwehe

$$\left(x-16\right)\left(x+10\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-160. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-6 ab=1\left(-160\right)=-160$$

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 -160.

$$1,-160 2,-80 4,-40 5,-32 8,-20 10,-16$$

Tātaihia te tapeke mō ia takirua.

$$1-160=-159 2-80=-78 4-40=-36 5-32=-27 8-20=-12 10-16=-6$$

Ko te otinga te takirua ka hoatu i te tapeke -6.

$$a=-16 b=10$$

Tuhia anō te x^{2}-6x-160 hei \left(x^{2}-16x\right)+\left(10x-160\right).

$$\left(x^{2}-16x\right)+\left(10x-160\right)$$

Tauwehea te x i te tuatahi me te 10 i te rōpū tuarua.

$$x\left(x-16\right)+10\left(x-16\right)$$

Whakatauwehea atu te kīanga pātahi x-16 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-16\right)\left(x+10\right)$$

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.

$$x^{2}-6x-160=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-160\right)}}{2}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-160\right)}}{2}$$

Whakareatia -4 ki te -160.

$$x=\frac{-\left(-6\right)±\sqrt{36+640}}{2}$$

Tāpiri 36 ki te 640.

$$x=\frac{-\left(-6\right)±\sqrt{676}}{2}$$

Tuhia te pūtakerua o te 676.

$$x=\frac{-\left(-6\right)±26}{2}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±26}{2}$$

Nā, me whakaoti te whārite x=\frac{6±26}{2} ina he tāpiri te ±. Tāpiri 6 ki te 26.

$$x=\frac{32}{2}$$

Whakawehe 32 ki te 2.

$$x=16$$

Nā, me whakaoti te whārite x=\frac{6±26}{2} ina he tango te ±. Tango 26 mai i 6.

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

Whakawehe -20 ki te 2.

$$x=-10$$

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 16 mō te x_{1} me te -10 mō te x_{2}.

$$x^{2}-6x-160=\left(x-16\right)\left(x-\left(-10\right)\right)$$

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

$$x^{2}-6x-160=\left(x-16\right)\left(x+10\right)$$

Aromātai

$$\left(x-16\right)\left(x+10\right)$$