Whakaoti i te x^2+10x+5

$$x ^ { 2 } + 10 x + 5$$

Tauwehe

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

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.

$$x^{2}+10x+5=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}-4\times 5}}{2}$$

Pūrua 10.

$$x=\frac{-10±\sqrt{100-4\times 5}}{2}$$

Whakareatia -4 ki te 5.

$$x=\frac{-10±\sqrt{100-20}}{2}$$

Tāpiri 100 ki te -20.

$$x=\frac{-10±\sqrt{80}}{2}$$

Tuhia te pūtakerua o te 80.

$$x=\frac{-10±4\sqrt{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{-10±4\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri -10 ki te 4\sqrt{5}.

$$x=\frac{4\sqrt{5}-10}{2}$$

Whakawehe -10+4\sqrt{5} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{-10±4\sqrt{5}}{2} ina he tango te ±. Tango 4\sqrt{5} mai i -10.

$$x=\frac{-4\sqrt{5}-10}{2}$$

Whakawehe -10-4\sqrt{5} ki te 2.

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

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}.

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

Aromātai

$$x^{2}+10x+5$$