Whakaoti i te -49t^2+55t+3

$$-49 { t }^{ 2 } +55t+3$$

Tauwehe

$$-49\left(t-\frac{55-\sqrt{3613}}{98}\right)\left(t-\frac{\sqrt{3613}+55}{98}\right)$$

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.

$$-49t^{2}+55t+3=0$$

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.

$$t=\frac{-55±\sqrt{55^{2}-4\left(-49\right)\times 3}}{2\left(-49\right)}$$

Pūrua 55.

$$t=\frac{-55±\sqrt{3025-4\left(-49\right)\times 3}}{2\left(-49\right)}$$

Whakareatia -4 ki te -49.

$$t=\frac{-55±\sqrt{3025+196\times 3}}{2\left(-49\right)}$$

Whakareatia 196 ki te 3.

$$t=\frac{-55±\sqrt{3025+588}}{2\left(-49\right)}$$

Tāpiri 3025 ki te 588.

$$t=\frac{-55±\sqrt{3613}}{2\left(-49\right)}$$

Whakareatia 2 ki te -49.

$$t=\frac{-55±\sqrt{3613}}{-98}$$

Nā, me whakaoti te whārite t=\frac{-55±\sqrt{3613}}{-98} ina he tāpiri te ±. Tāpiri -55 ki te \sqrt{3613}.

$$t=\frac{\sqrt{3613}-55}{-98}$$

Whakawehe -55+\sqrt{3613} ki te -98.

$$t=\frac{55-\sqrt{3613}}{98}$$

Nā, me whakaoti te whārite t=\frac{-55±\sqrt{3613}}{-98} ina he tango te ±. Tango \sqrt{3613} mai i -55.

$$t=\frac{-\sqrt{3613}-55}{-98}$$

Whakawehe -55-\sqrt{3613} ki te -98.

$$t=\frac{\sqrt{3613}+55}{98}$$

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{55-\sqrt{3613}}{98} mō te x_{1} me te \frac{55+\sqrt{3613}}{98} mō te x_{2}.

$$-49t^{2}+55t+3=-49\left(t-\frac{55-\sqrt{3613}}{98}\right)\left(t-\frac{\sqrt{3613}+55}{98}\right)$$

Aromātai

$$3+55t-49t^{2}$$