Whakaoti i te 4x^2+2x-40

$$4 { x }^{ 2 } +2x-40$$

Tauwehe

$$4\left(x-\frac{-\sqrt{161}-1}{4}\right)\left(x-\frac{\sqrt{161}-1}{4}\right)$$

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.

$$4x^{2}+2x-40=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 4\left(-40\right)}}{2\times 4}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 4\left(-40\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-2±\sqrt{4-16\left(-40\right)}}{2\times 4}$$

Whakareatia -16 ki te -40.

$$x=\frac{-2±\sqrt{4+640}}{2\times 4}$$

Tāpiri 4 ki te 640.

$$x=\frac{-2±\sqrt{644}}{2\times 4}$$

Tuhia te pūtakerua o te 644.

$$x=\frac{-2±2\sqrt{161}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-2±2\sqrt{161}}{8}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{161}}{8} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{161}.

$$x=\frac{2\sqrt{161}-2}{8}$$

Whakawehe -2+2\sqrt{161} ki te 8.

$$x=\frac{\sqrt{161}-1}{4}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{161}}{8} ina he tango te ±. Tango 2\sqrt{161} mai i -2.

$$x=\frac{-2\sqrt{161}-2}{8}$$

Whakawehe -2-2\sqrt{161} ki te 8.

$$x=\frac{-\sqrt{161}-1}{4}$$

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{-1+\sqrt{161}}{4} mō te x_{1} me te \frac{-1-\sqrt{161}}{4} mō te x_{2}.

$$4x^{2}+2x-40=4\left(x-\frac{\sqrt{161}-1}{4}\right)\left(x-\frac{-\sqrt{161}-1}{4}\right)$$

Aromātai

$$2\left(2x^{2}+x-20\right)$$