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

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

Tauwehe

$$5\left(x-\frac{-\sqrt{89}-7}{10}\right)\left(x-\frac{\sqrt{89}-7}{10}\right)$$

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.

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

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.

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

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\times 5\left(-2\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-7±\sqrt{49-20\left(-2\right)}}{2\times 5}$$

Whakareatia -20 ki te -2.

$$x=\frac{-7±\sqrt{49+40}}{2\times 5}$$

Tāpiri 49 ki te 40.

$$x=\frac{-7±\sqrt{89}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-7±\sqrt{89}}{10}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{89}}{10} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{89}.

$$x=\frac{\sqrt{89}-7}{10}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{89}}{10} ina he tango te ±. Tango \sqrt{89} mai i -7.

$$x=\frac{-\sqrt{89}-7}{10}$$

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{-7+\sqrt{89}}{10} mō te x_{1} me te \frac{-7-\sqrt{89}}{10} mō te x_{2}.

$$5x^{2}+7x-2=5\left(x-\frac{\sqrt{89}-7}{10}\right)\left(x-\frac{-\sqrt{89}-7}{10}\right)$$

Aromātai

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