Whakaoti i te 5x^2+8x-7

$$5 x ^ { 2 } + 8 x - 7$$

Tauwehe

$$5\left(x-\frac{-\sqrt{51}-4}{5}\right)\left(x-\frac{\sqrt{51}-4}{5}\right)$$

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.

$$5x^{2}+8x-7=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 5\left(-7\right)}}{2\times 5}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 5\left(-7\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-8±\sqrt{64-20\left(-7\right)}}{2\times 5}$$

Whakareatia -20 ki te -7.

$$x=\frac{-8±\sqrt{64+140}}{2\times 5}$$

Tāpiri 64 ki te 140.

$$x=\frac{-8±\sqrt{204}}{2\times 5}$$

Tuhia te pūtakerua o te 204.

$$x=\frac{-8±2\sqrt{51}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-8±2\sqrt{51}}{10}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{51}}{10} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{51}.

$$x=\frac{2\sqrt{51}-8}{10}$$

Whakawehe -8+2\sqrt{51} ki te 10.

$$x=\frac{\sqrt{51}-4}{5}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{51}}{10} ina he tango te ±. Tango 2\sqrt{51} mai i -8.

$$x=\frac{-2\sqrt{51}-8}{10}$$

Whakawehe -8-2\sqrt{51} ki te 10.

$$x=\frac{-\sqrt{51}-4}{5}$$

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 \frac{-4+\sqrt{51}}{5} mō te x_{1} me te \frac{-4-\sqrt{51}}{5} mō te x_{2}.

$$5x^{2}+8x-7=5\left(x-\frac{\sqrt{51}-4}{5}\right)\left(x-\frac{-\sqrt{51}-4}{5}\right)$$

Aromātai

$$5x^{2}+8x-7$$