Whakaoti i te 5x^2+20x-2

$$5 { x }^{ 2 } +20x-2$$

Tauwehe

$$5\left(x-\left(-\frac{\sqrt{110}}{5}-2\right)\right)\left(x-\left(\frac{\sqrt{110}}{5}-2\right)\right)$$

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.

$$5x^{2}+20x-2=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\times 5\left(-2\right)}}{2\times 5}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\times 5\left(-2\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-20±\sqrt{400-20\left(-2\right)}}{2\times 5}$$

Whakareatia -20 ki te -2.

$$x=\frac{-20±\sqrt{400+40}}{2\times 5}$$

Tāpiri 400 ki te 40.

$$x=\frac{-20±\sqrt{440}}{2\times 5}$$

Tuhia te pūtakerua o te 440.

$$x=\frac{-20±2\sqrt{110}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-20±2\sqrt{110}}{10}$$

Nā, me whakaoti te whārite x=\frac{-20±2\sqrt{110}}{10} ina he tāpiri te ±. Tāpiri -20 ki te 2\sqrt{110}.

$$x=\frac{2\sqrt{110}-20}{10}$$

Whakawehe -20+2\sqrt{110} ki te 10.

$$x=\frac{\sqrt{110}}{5}-2$$

Nā, me whakaoti te whārite x=\frac{-20±2\sqrt{110}}{10} ina he tango te ±. Tango 2\sqrt{110} mai i -20.

$$x=\frac{-2\sqrt{110}-20}{10}$$

Whakawehe -20-2\sqrt{110} ki te 10.

$$x=-\frac{\sqrt{110}}{5}-2$$

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 -2+\frac{\sqrt{110}}{5} mō te x_{1} me te -2-\frac{\sqrt{110}}{5} mō te x_{2}.

$$5x^{2}+20x-2=5\left(x-\left(\frac{\sqrt{110}}{5}-2\right)\right)\left(x-\left(-\frac{\sqrt{110}}{5}-2\right)\right)$$

Aromātai

$$5x^{2}+20x-2$$