Whakaoti i te 2x^2-4x-6=

$$2 x ^ { 2 } - 4 x - 6 =$$

Tauwehe

$$2\left(x-3\right)\left(x+1\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(x^{2}-2x-3\right)$$

Whakaarohia te x^{2}-2x-3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=1\left(-3\right)=-3$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-3 b=1$$

Tuhia anō te x^{2}-2x-3 hei \left(x^{2}-3x\right)+\left(x-3\right).

$$\left(x^{2}-3x\right)+\left(x-3\right)$$

Whakatauwehea atu x i te x^{2}-3x.

$$x\left(x-3\right)+x-3$$

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-3\right)\left(x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x-3\right)\left(x+1\right)$$

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.

$$2x^{2}-4x-6=0$$

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.

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

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-6\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-6\right)}}{2\times 2}$$

Whakareatia -8 ki te -6.

$$x=\frac{-\left(-4\right)±\sqrt{16+48}}{2\times 2}$$

Tāpiri 16 ki te 48.

$$x=\frac{-\left(-4\right)±\sqrt{64}}{2\times 2}$$

Tuhia te pūtakerua o te 64.

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

Ko te tauaro o -4 ko 4.

$$x=\frac{4±8}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{4±8}{4}$$

Nā, me whakaoti te whārite x=\frac{4±8}{4} ina he tāpiri te ±. Tāpiri 4 ki te 8.

$$x=\frac{12}{4}$$

Whakawehe 12 ki te 4.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{4±8}{4} ina he tango te ±. Tango 8 mai i 4.

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

Whakawehe -4 ki te 4.

$$x=-1$$

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 3 mō te x_{1} me te -1 mō te x_{2}.

$$2x^{2}-4x-6=2\left(x-3\right)\left(x-\left(-1\right)\right)$$

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

$$2x^{2}-4x-6=2\left(x-3\right)\left(x+1\right)$$

Aromātai

$$2\left(x-3\right)\left(x+1\right)$$