Whakaoti i te 5t^2+10t

$$5 t ^ { 2 } + 10 t$$

Tauwehe

$$5t\left(t+2\right)$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(t^{2}+2t\right)$$

Whakaarohia te t^{2}+2t. Tauwehea te t.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$5t\left(t+2\right)$$

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.

$$5t^{2}+10t=0$$

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.

$$t=\frac{-10±\sqrt{10^{2}}}{2\times 5}$$

Tuhia te pūtakerua o te 10^{2}.

$$t=\frac{-10±10}{2\times 5}$$

Whakareatia 2 ki te 5.

$$t=\frac{-10±10}{10}$$

Nā, me whakaoti te whārite t=\frac{-10±10}{10} ina he tāpiri te ±. Tāpiri -10 ki te 10.

$$t=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$t=0$$

Nā, me whakaoti te whārite t=\frac{-10±10}{10} ina he tango te ±. Tango 10 mai i -10.

$$t=-\frac{20}{10}$$

Whakawehe -20 ki te 10.

$$t=-2$$

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 0 mō te x_{1} me te -2 mō te x_{2}.

$$5t^{2}+10t=5t\left(t-\left(-2\right)\right)$$

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

$$5t^{2}+10t=5t\left(t+2\right)$$

Aromātai

$$5t\left(t+2\right)$$