Whakaoti i te -2x^2+26x-24

$$- 2 x ^ { 2 } + 26 x - 24$$

Tauwehe

$$2\left(1-x\right)\left(x-12\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(-x^{2}+13x-12\right)$$

Whakaarohia te -x^{2}+13x-12. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx-12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=13 ab=-\left(-12\right)=12$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.

$$1,12 2,6 3,4$$

Tātaihia te tapeke mō ia takirua.

$$1+12=13 2+6=8 3+4=7$$

Ko te otinga te takirua ka hoatu i te tapeke 13.

$$a=12 b=1$$

Tuhia anō te -x^{2}+13x-12 hei \left(-x^{2}+12x\right)+\left(x-12\right).

$$\left(-x^{2}+12x\right)+\left(x-12\right)$$

Whakatauwehea atu -x i te -x^{2}+12x.

$$-x\left(x-12\right)+x-12$$

Whakatauwehea atu te kīanga pātahi x-12 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-12\right)\left(-x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x-12\right)\left(-x+1\right)$$

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.

$$-2x^{2}+26x-24=0$$

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.

$$x=\frac{-26±\sqrt{26^{2}-4\left(-2\right)\left(-24\right)}}{2\left(-2\right)}$$

Pūrua 26.

$$x=\frac{-26±\sqrt{676-4\left(-2\right)\left(-24\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-26±\sqrt{676+8\left(-24\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -24.

$$x=\frac{-26±\sqrt{676-192}}{2\left(-2\right)}$$

Tāpiri 676 ki te -192.

$$x=\frac{-26±\sqrt{484}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 484.

$$x=\frac{-26±22}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-26±22}{-4}$$

Nā, me whakaoti te whārite x=\frac{-26±22}{-4} ina he tāpiri te ±. Tāpiri -26 ki te 22.

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

Whakawehe -4 ki te -4.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-26±22}{-4} ina he tango te ±. Tango 22 mai i -26.

$$x=-\frac{48}{-4}$$

Whakawehe -48 ki te -4.

$$x=12$$

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 12 mō te x_{2}.

$$-2x^{2}+26x-24=-2\left(x-1\right)\left(x-12\right)$$

Aromātai

$$2\left(1-x\right)\left(x-12\right)$$