Whakaoti i te 14x^2+12x-2

$$14 x ^ { 2 } + 12 x - 2$$

Tauwehe

$$2\left(7x-1\right)\left(x+1\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(7x^{2}+6x-1\right)$$

Whakaarohia te 7x^{2}+6x-1. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 7x^{2}+ax+bx-1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=7\left(-1\right)=-7$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=7$$

Tuhia anō te 7x^{2}+6x-1 hei \left(7x^{2}-x\right)+\left(7x-1\right).

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

Whakatauwehea atu x i te 7x^{2}-x.

$$x\left(7x-1\right)+7x-1$$

Whakatauwehea atu te kīanga pātahi 7x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(7x-1\right)\left(x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(7x-1\right)\left(x+1\right)$$

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.

$$14x^{2}+12x-2=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 14\left(-2\right)}}{2\times 14}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 14\left(-2\right)}}{2\times 14}$$

Whakareatia -4 ki te 14.

$$x=\frac{-12±\sqrt{144-56\left(-2\right)}}{2\times 14}$$

Whakareatia -56 ki te -2.

$$x=\frac{-12±\sqrt{144+112}}{2\times 14}$$

Tāpiri 144 ki te 112.

$$x=\frac{-12±\sqrt{256}}{2\times 14}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{-12±16}{2\times 14}$$

Whakareatia 2 ki te 14.

$$x=\frac{-12±16}{28}$$

Nā, me whakaoti te whārite x=\frac{-12±16}{28} ina he tāpiri te ±. Tāpiri -12 ki te 16.

$$x=\frac{4}{28}$$

Whakahekea te hautanga \frac{4}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{1}{7}$$

Nā, me whakaoti te whārite x=\frac{-12±16}{28} ina he tango te ±. Tango 16 mai i -12.

$$x=-\frac{28}{28}$$

Whakawehe -28 ki te 28.

$$x=-1$$

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 \frac{1}{7} mō te x_{1} me te -1 mō te x_{2}.

$$14x^{2}+12x-2=14\left(x-\frac{1}{7}\right)\left(x-\left(-1\right)\right)$$

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

$$14x^{2}+12x-2=14\left(x-\frac{1}{7}\right)\left(x+1\right)$$

Tango \frac{1}{7} mai i x mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$14x^{2}+12x-2=14\times \frac{7x-1}{7}\left(x+1\right)$$

Whakakorea atu te tauwehe pūnoa nui rawa 7 i roto i te 14 me te 7.

$$14x^{2}+12x-2=2\left(7x-1\right)\left(x+1\right)$$

Aromātai

$$2\left(7x-1\right)\left(x+1\right)$$