Whakaoti i te x^2+20x-15

$$x ^ { 2 } + 20 x - 15$$

Tauwehe

$$\left(x-\left(-\sqrt{115}-10\right)\right)\left(x-\left(\sqrt{115}-10\right)\right)$$

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.

$$x^{2}+20x-15=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-15\right)}}{2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$x=\frac{-20±\sqrt{400+60}}{2}$$

Tāpiri 400 ki te 60.

$$x=\frac{-20±\sqrt{460}}{2}$$

Tuhia te pūtakerua o te 460.

$$x=\frac{-20±2\sqrt{115}}{2}$$

Nā, me whakaoti te whārite x=\frac{-20±2\sqrt{115}}{2} ina he tāpiri te ±. Tāpiri -20 ki te 2\sqrt{115}.

$$x=\frac{2\sqrt{115}-20}{2}$$

Whakawehe -20+2\sqrt{115} ki te 2.

$$x=\sqrt{115}-10$$

Nā, me whakaoti te whārite x=\frac{-20±2\sqrt{115}}{2} ina he tango te ±. Tango 2\sqrt{115} mai i -20.

$$x=\frac{-2\sqrt{115}-20}{2}$$

Whakawehe -20-2\sqrt{115} ki te 2.

$$x=-\sqrt{115}-10$$

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 -10+\sqrt{115} mō te x_{1} me te -10-\sqrt{115} mō te x_{2}.

$$x^{2}+20x-15=\left(x-\left(\sqrt{115}-10\right)\right)\left(x-\left(-\sqrt{115}-10\right)\right)$$

Aromātai

$$x^{2}+20x-15$$