Whakaoti i te 38t^2-3,403t+65,590

$$38 t ^ { 2 } - 3,403 t + 65,590$$

Tauwehe

$$38\left(t-\frac{3403-\sqrt{1610729}}{76}\right)\left(t-\frac{\sqrt{1610729}+3403}{76}\right)$$

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.

$$38t^{2}-3403t+65590=0$$

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.

$$t=\frac{-\left(-3403\right)±\sqrt{\left(-3403\right)^{2}-4\times 38\times 65590}}{2\times 38}$$

Pūrua -3403.

$$t=\frac{-\left(-3403\right)±\sqrt{11580409-4\times 38\times 65590}}{2\times 38}$$

Whakareatia -4 ki te 38.

$$t=\frac{-\left(-3403\right)±\sqrt{11580409-152\times 65590}}{2\times 38}$$

Whakareatia -152 ki te 65590.

$$t=\frac{-\left(-3403\right)±\sqrt{11580409-9969680}}{2\times 38}$$

Tāpiri 11580409 ki te -9969680.

$$t=\frac{-\left(-3403\right)±\sqrt{1610729}}{2\times 38}$$

Ko te tauaro o -3403 ko 3403.

$$t=\frac{3403±\sqrt{1610729}}{2\times 38}$$

Whakareatia 2 ki te 38.

$$t=\frac{3403±\sqrt{1610729}}{76}$$

Nā, me whakaoti te whārite t=\frac{3403±\sqrt{1610729}}{76} ina he tāpiri te ±. Tāpiri 3403 ki te \sqrt{1610729}.

$$t=\frac{\sqrt{1610729}+3403}{76}$$

Nā, me whakaoti te whārite t=\frac{3403±\sqrt{1610729}}{76} ina he tango te ±. Tango \sqrt{1610729} mai i 3403.

$$t=\frac{3403-\sqrt{1610729}}{76}$$

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 \frac{3403+\sqrt{1610729}}{76} mō te x_{1} me te \frac{3403-\sqrt{1610729}}{76} mō te x_{2}.

$$38t^{2}-3403t+65590=38\left(t-\frac{\sqrt{1610729}+3403}{76}\right)\left(t-\frac{3403-\sqrt{1610729}}{76}\right)$$

Aromātai

$$38t^{2}-3403t+65590$$