Whakaoti i te 20x+2x^2+10

$$20x+2 { x }^{ 2 } +10$$

Tauwehe

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

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.

$$2x^{2}+20x+10=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\times 2\times 10}}{2\times 2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\times 2\times 10}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-20±\sqrt{400-8\times 10}}{2\times 2}$$

Whakareatia -8 ki te 10.

$$x=\frac{-20±\sqrt{400-80}}{2\times 2}$$

Tāpiri 400 ki te -80.

$$x=\frac{-20±\sqrt{320}}{2\times 2}$$

Tuhia te pūtakerua o te 320.

$$x=\frac{-20±8\sqrt{5}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-20±8\sqrt{5}}{4}$$

Nā, me whakaoti te whārite x=\frac{-20±8\sqrt{5}}{4} ina he tāpiri te ±. Tāpiri -20 ki te 8\sqrt{5}.

$$x=\frac{8\sqrt{5}-20}{4}$$

Whakawehe -20+8\sqrt{5} ki te 4.

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

Nā, me whakaoti te whārite x=\frac{-20±8\sqrt{5}}{4} ina he tango te ±. Tango 8\sqrt{5} mai i -20.

$$x=\frac{-8\sqrt{5}-20}{4}$$

Whakawehe -20-8\sqrt{5} ki te 4.

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

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

$$2x^{2}+20x+10=2\left(x-\left(2\sqrt{5}-5\right)\right)\left(x-\left(-2\sqrt{5}-5\right)\right)$$

Aromātai

$$2\left(x^{2}+10x+5\right)$$