Whakaoti i te -2x^2-22x+24

$$- 2 x ^ { 2 } - 22 x + 24$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(-x^{2}-11x+12\right)$$

Whakaarohia te -x^{2}-11x+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.

$$a+b=-11 ab=-12=-12$$

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 -12.

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

Tātaihia te tapeke mō ia takirua.

$$1-12=-11 2-6=-4 3-4=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=1 b=-12$$

Tuhia anō te -x^{2}-11x+12 hei \left(-x^{2}+x\right)+\left(-12x+12\right).

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

Tauwehea te x i te tuatahi me te 12 i te rōpū tuarua.

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

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.

$$-2x^{2}-22x+24=0$$

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.

$$x=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\left(-2\right)\times 24}}{2\left(-2\right)}$$

Pūrua -22.

$$x=\frac{-\left(-22\right)±\sqrt{484-4\left(-2\right)\times 24}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-\left(-22\right)±\sqrt{484+8\times 24}}{2\left(-2\right)}$$

Whakareatia 8 ki te 24.

$$x=\frac{-\left(-22\right)±\sqrt{484+192}}{2\left(-2\right)}$$

Tāpiri 484 ki te 192.

$$x=\frac{-\left(-22\right)±\sqrt{676}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 676.

$$x=\frac{-\left(-22\right)±26}{2\left(-2\right)}$$

Ko te tauaro o -22 ko 22.

$$x=\frac{22±26}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{22±26}{-4}$$

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

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

Whakawehe 48 ki te -4.

$$x=-12$$

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

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

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 -12 mō te x_{1} me te 1 mō te x_{2}.

$$-2x^{2}-22x+24=-2\left(x-\left(-12\right)\right)\left(x-1\right)$$

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

$$-2x^{2}-22x+24=-2\left(x+12\right)\left(x-1\right)$$

Aromātai

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