Whakaoti i te 3t-28+t^2

$$3 t - 28 + t ^ { 2 }$$

Tauwehe

$$\left(t-4\right)\left(t+7\right)$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$t^{2}+3t-28$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei t^{2}+at+bt-28. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=1\left(-28\right)=-28$$

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 -28.

$$-1,28 -2,14 -4,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+28=27 -2+14=12 -4+7=3$$

Ko te otinga te takirua ka hoatu i te tapeke 3.

$$a=-4 b=7$$

Tuhia anō te t^{2}+3t-28 hei \left(t^{2}-4t\right)+\left(7t-28\right).

$$\left(t^{2}-4t\right)+\left(7t-28\right)$$

Tauwehea te t i te tuatahi me te 7 i te rōpū tuarua.

$$t\left(t-4\right)+7\left(t-4\right)$$

Whakatauwehea atu te kīanga pātahi t-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(t-4\right)\left(t+7\right)$$

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.

$$t^{2}+3t-28=0$$

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.

$$t=\frac{-3±\sqrt{3^{2}-4\left(-28\right)}}{2}$$

Pūrua 3.

$$t=\frac{-3±\sqrt{9-4\left(-28\right)}}{2}$$

Whakareatia -4 ki te -28.

$$t=\frac{-3±\sqrt{9+112}}{2}$$

Tāpiri 9 ki te 112.

$$t=\frac{-3±\sqrt{121}}{2}$$

Tuhia te pūtakerua o te 121.

$$t=\frac{-3±11}{2}$$

Nā, me whakaoti te whārite t=\frac{-3±11}{2} ina he tāpiri te ±. Tāpiri -3 ki te 11.

$$t=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$t=4$$

Nā, me whakaoti te whārite t=\frac{-3±11}{2} ina he tango te ±. Tango 11 mai i -3.

$$t=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$t=-7$$

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 -7 mō te x_{2}.

$$t^{2}+3t-28=\left(t-4\right)\left(t-\left(-7\right)\right)$$

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

$$t^{2}+3t-28=\left(t-4\right)\left(t+7\right)$$

Aromātai

$$\left(t-4\right)\left(t+7\right)$$