Whakaoti i te 2x^2+14x-16

$$2 { x }^{ 2 } +14x-16$$

Tauwehe

$$2\left(x-1\right)\left(x+8\right)$$

Ngā Upane Otinga

Tauwehea te 2.

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

Whakaarohia te x^{2}+7x-8. 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 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 -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.

$$a=-1 b=8$$

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

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

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

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

Whakatauwehea atu te kīanga pātahi x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x-1\right)\left(x+8\right)$$

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.

$$2x^{2}+14x-16=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\times 2\left(-16\right)}}{2\times 2}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\times 2\left(-16\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-14±\sqrt{196-8\left(-16\right)}}{2\times 2}$$

Whakareatia -8 ki te -16.

$$x=\frac{-14±\sqrt{196+128}}{2\times 2}$$

Tāpiri 196 ki te 128.

$$x=\frac{-14±\sqrt{324}}{2\times 2}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{-14±18}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-14±18}{4}$$

Nā, me whakaoti te whārite x=\frac{-14±18}{4} ina he tāpiri te ±. Tāpiri -14 ki te 18.

$$x=\frac{4}{4}$$

Whakawehe 4 ki te 4.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-14±18}{4} ina he tango te ±. Tango 18 mai i -14.

$$x=-\frac{32}{4}$$

Whakawehe -32 ki te 4.

$$x=-8$$

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 1 mō te x_{1} me te -8 mō te x_{2}.

$$2x^{2}+14x-16=2\left(x-1\right)\left(x-\left(-8\right)\right)$$

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

$$2x^{2}+14x-16=2\left(x-1\right)\left(x+8\right)$$

Aromātai

$$2\left(x-1\right)\left(x+8\right)$$