Whakaoti i te 6t^2-9t-6=

$$6 t ^ { 2 } - 9 t - 6 =$$

Tauwehe

$$3\left(t-2\right)\left(2t+1\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(2t^{2}-3t-2\right)$$

Whakaarohia te 2t^{2}-3t-2. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2t^{2}+at+bt-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-3 ab=2\left(-2\right)=-4$$

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 -4.

$$1,-4 2,-2$$

Tātaihia te tapeke mō ia takirua.

$$1-4=-3 2-2=0$$

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

$$a=-4 b=1$$

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

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

Whakatauwehea atu 2t i te 2t^{2}-4t.

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

Whakatauwehea atu te kīanga pātahi t-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(t-2\right)\left(2t+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(t-2\right)\left(2t+1\right)$$

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.

$$6t^{2}-9t-6=0$$

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.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 6\left(-6\right)}}{2\times 6}$$

Pūrua -9.

$$t=\frac{-\left(-9\right)±\sqrt{81-4\times 6\left(-6\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$t=\frac{-\left(-9\right)±\sqrt{81-24\left(-6\right)}}{2\times 6}$$

Whakareatia -24 ki te -6.

$$t=\frac{-\left(-9\right)±\sqrt{81+144}}{2\times 6}$$

Tāpiri 81 ki te 144.

$$t=\frac{-\left(-9\right)±\sqrt{225}}{2\times 6}$$

Tuhia te pūtakerua o te 225.

$$t=\frac{-\left(-9\right)±15}{2\times 6}$$

Ko te tauaro o -9 ko 9.

$$t=\frac{9±15}{2\times 6}$$

Whakareatia 2 ki te 6.

$$t=\frac{9±15}{12}$$

Nā, me whakaoti te whārite t=\frac{9±15}{12} ina he tāpiri te ±. Tāpiri 9 ki te 15.

$$t=\frac{24}{12}$$

Whakawehe 24 ki te 12.

$$t=2$$

Nā, me whakaoti te whārite t=\frac{9±15}{12} ina he tango te ±. Tango 15 mai i 9.

$$t=-\frac{6}{12}$$

Whakahekea te hautanga \frac{-6}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$t=-\frac{1}{2}$$

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

$$6t^{2}-9t-6=6\left(t-2\right)\left(t-\left(-\frac{1}{2}\right)\right)$$

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

$$6t^{2}-9t-6=6\left(t-2\right)\left(t+\frac{1}{2}\right)$$

Tāpiri \frac{1}{2} ki te t mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$6t^{2}-9t-6=6\left(t-2\right)\times \frac{2t+1}{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 6 me te 2.

$$6t^{2}-9t-6=3\left(t-2\right)\left(2t+1\right)$$

Aromātai

$$3\left(t-2\right)\left(2t+1\right)$$