Whakaoti i te 80t-16t^2

$$80 t - 16 t ^ { 2 }$$

Tauwehe

$$16t\left(5-t\right)$$

Ngā Upane Otinga

Tauwehea te 16.

$$16\left(5t-t^{2}\right)$$

Whakaarohia te 5t-t^{2}. Tauwehea te t.

$$t\left(5-t\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$16t\left(-t+5\right)$$

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.

$$-16t^{2}+80t=0$$

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.

$$t=\frac{-80±\sqrt{80^{2}}}{2\left(-16\right)}$$

Tuhia te pūtakerua o te 80^{2}.

$$t=\frac{-80±80}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$t=\frac{-80±80}{-32}$$

Nā, me whakaoti te whārite t=\frac{-80±80}{-32} ina he tāpiri te ±. Tāpiri -80 ki te 80.

$$t=\frac{0}{-32}$$

Whakawehe 0 ki te -32.

$$t=0$$

Nā, me whakaoti te whārite t=\frac{-80±80}{-32} ina he tango te ±. Tango 80 mai i -80.

$$t=-\frac{160}{-32}$$

Whakawehe -160 ki te -32.

$$t=5$$

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 5 mō te x_{2}.

$$-16t^{2}+80t=-16t\left(t-5\right)$$

Aromātai

$$16t\left(5-t\right)$$