Whakaoti i te (-2t^2-7t+5)+(-8t^2+4t-3)

$$( - 2 t ^ { 2 } - 7 t + 5 ) + ( - 8 t ^ { 2 } + 4 t - 3 )$$

Aromātai

$$2-3t-10t^{2}$$

Ngā Upane Otinga

Pahekotia te -2t^{2} me -8t^{2}, ka -10t^{2}.

$$-10t^{2}-7t+5+4t-3$$

Pahekotia te -7t me 4t, ka -3t.

$$-10t^{2}-3t+5-3$$

Tangohia te 3 i te 5, ka 2.

$$-10t^{2}-3t+2$$

Tauwehe

$$-10\left(t-\frac{-\sqrt{89}-3}{20}\right)\left(t-\frac{\sqrt{89}-3}{20}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -2t^{2} me -8t^{2}, ka -10t^{2}.

$$factor(-10t^{2}-7t+5+4t-3)$$

Pahekotia te -7t me 4t, ka -3t.

$$factor(-10t^{2}-3t+5-3)$$

Tangohia te 3 i te 5, ka 2.

$$factor(-10t^{2}-3t+2)$$

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.

$$-10t^{2}-3t+2=0$$

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.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-10\right)\times 2}}{2\left(-10\right)}$$

Pūrua -3.

$$t=\frac{-\left(-3\right)±\sqrt{9-4\left(-10\right)\times 2}}{2\left(-10\right)}$$

Whakareatia -4 ki te -10.

$$t=\frac{-\left(-3\right)±\sqrt{9+40\times 2}}{2\left(-10\right)}$$

Whakareatia 40 ki te 2.

$$t=\frac{-\left(-3\right)±\sqrt{9+80}}{2\left(-10\right)}$$

Tāpiri 9 ki te 80.

$$t=\frac{-\left(-3\right)±\sqrt{89}}{2\left(-10\right)}$$

Ko te tauaro o -3 ko 3.

$$t=\frac{3±\sqrt{89}}{2\left(-10\right)}$$

Whakareatia 2 ki te -10.

$$t=\frac{3±\sqrt{89}}{-20}$$

Nā, me whakaoti te whārite t=\frac{3±\sqrt{89}}{-20} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{89}.

$$t=\frac{\sqrt{89}+3}{-20}$$

Whakawehe 3+\sqrt{89} ki te -20.

$$t=\frac{-\sqrt{89}-3}{20}$$

Nā, me whakaoti te whārite t=\frac{3±\sqrt{89}}{-20} ina he tango te ±. Tango \sqrt{89} mai i 3.

$$t=\frac{3-\sqrt{89}}{-20}$$

Whakawehe 3-\sqrt{89} ki te -20.

$$t=\frac{\sqrt{89}-3}{20}$$

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{-3-\sqrt{89}}{20} mō te x_{1} me te \frac{-3+\sqrt{89}}{20} mō te x_{2}.

$$-10t^{2}-3t+2=-10\left(t-\frac{-\sqrt{89}-3}{20}\right)\left(t-\frac{\sqrt{89}-3}{20}\right)$$