Whakaoti i te 2a^2+8a-13+3a^2-11a-5

$$2 a ^ { 2 } + 8 a - 13 + 3 a ^ { 2 } - 11 a - 5$$

Aromātai

$$5a^{2}-3a-18$$

Ngā Upane Otinga

Pahekotia te 2a^{2} me 3a^{2}, ka 5a^{2}.

$$5a^{2}+8a-13-11a-5$$

Pahekotia te 8a me -11a, ka -3a.

$$5a^{2}-3a-13-5$$

Tangohia te 5 i te -13, ka -18.

$$5a^{2}-3a-18$$

Tauwehe

$$5\left(a-\frac{3-3\sqrt{41}}{10}\right)\left(a-\frac{3\sqrt{41}+3}{10}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 2a^{2} me 3a^{2}, ka 5a^{2}.

$$factor(5a^{2}+8a-13-11a-5)$$

Pahekotia te 8a me -11a, ka -3a.

$$factor(5a^{2}-3a-13-5)$$

Tangohia te 5 i te -13, ka -18.

$$factor(5a^{2}-3a-18)$$

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.

$$5a^{2}-3a-18=0$$

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.

$$a=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 5\left(-18\right)}}{2\times 5}$$

Pūrua -3.

$$a=\frac{-\left(-3\right)±\sqrt{9-4\times 5\left(-18\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$a=\frac{-\left(-3\right)±\sqrt{9-20\left(-18\right)}}{2\times 5}$$

Whakareatia -20 ki te -18.

$$a=\frac{-\left(-3\right)±\sqrt{9+360}}{2\times 5}$$

Tāpiri 9 ki te 360.

$$a=\frac{-\left(-3\right)±\sqrt{369}}{2\times 5}$$

Tuhia te pūtakerua o te 369.

$$a=\frac{-\left(-3\right)±3\sqrt{41}}{2\times 5}$$

Ko te tauaro o -3 ko 3.

$$a=\frac{3±3\sqrt{41}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$a=\frac{3±3\sqrt{41}}{10}$$

Nā, me whakaoti te whārite a=\frac{3±3\sqrt{41}}{10} ina he tāpiri te ±. Tāpiri 3 ki te 3\sqrt{41}.

$$a=\frac{3\sqrt{41}+3}{10}$$

Nā, me whakaoti te whārite a=\frac{3±3\sqrt{41}}{10} ina he tango te ±. Tango 3\sqrt{41} mai i 3.

$$a=\frac{3-3\sqrt{41}}{10}$$

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+3\sqrt{41}}{10} mō te x_{1} me te \frac{3-3\sqrt{41}}{10} mō te x_{2}.

$$5a^{2}-3a-18=5\left(a-\frac{3\sqrt{41}+3}{10}\right)\left(a-\frac{3-3\sqrt{41}}{10}\right)$$