Whakaoti i te -2t^2+12t+80

$$- 2 t ^ { 2 } + 12 t + 80$$

Tauwehe

$$-2\left(t-10\right)\left(t+4\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(-t^{2}+6t+40\right)$$

Whakaarohia te -t^{2}+6t+40. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -t^{2}+at+bt+40. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=-40=-40$$

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 -40.

$$-1,40 -2,20 -4,10 -5,8$$

Tātaihia te tapeke mō ia takirua.

$$-1+40=39 -2+20=18 -4+10=6 -5+8=3$$

Ko te otinga te takirua ka hoatu i te tapeke 6.

$$a=10 b=-4$$

Tuhia anō te -t^{2}+6t+40 hei \left(-t^{2}+10t\right)+\left(-4t+40\right).

$$\left(-t^{2}+10t\right)+\left(-4t+40\right)$$

Tauwehea te -t i te tuatahi me te -4 i te rōpū tuarua.

$$-t\left(t-10\right)-4\left(t-10\right)$$

Whakatauwehea atu te kīanga pātahi t-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(t-10\right)\left(-t-4\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(t-10\right)\left(-t-4\right)$$

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.

$$-2t^{2}+12t+80=0$$

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.

$$t=\frac{-12±\sqrt{12^{2}-4\left(-2\right)\times 80}}{2\left(-2\right)}$$

Pūrua 12.

$$t=\frac{-12±\sqrt{144-4\left(-2\right)\times 80}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$t=\frac{-12±\sqrt{144+8\times 80}}{2\left(-2\right)}$$

Whakareatia 8 ki te 80.

$$t=\frac{-12±\sqrt{144+640}}{2\left(-2\right)}$$

Tāpiri 144 ki te 640.

$$t=\frac{-12±\sqrt{784}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 784.

$$t=\frac{-12±28}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$t=\frac{-12±28}{-4}$$

Nā, me whakaoti te whārite t=\frac{-12±28}{-4} ina he tāpiri te ±. Tāpiri -12 ki te 28.

$$t=\frac{16}{-4}$$

Whakawehe 16 ki te -4.

$$t=-4$$

Nā, me whakaoti te whārite t=\frac{-12±28}{-4} ina he tango te ±. Tango 28 mai i -12.

$$t=-\frac{40}{-4}$$

Whakawehe -40 ki te -4.

$$t=10$$

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 -4 mō te x_{1} me te 10 mō te x_{2}.

$$-2t^{2}+12t+80=-2\left(t-\left(-4\right)\right)\left(t-10\right)$$

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

$$-2t^{2}+12t+80=-2\left(t+4\right)\left(t-10\right)$$

Aromātai

$$-2\left(t-10\right)\left(t+4\right)$$