Whakaoti i te 2x^2-10x-23

$$2 x ^ { 2 } - 10 x - 23$$

Tauwehe

$$2\left(x-\frac{5-\sqrt{71}}{2}\right)\left(x-\frac{\sqrt{71}+5}{2}\right)$$

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.

$$2x^{2}-10x-23=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\left(-23\right)}}{2\times 2}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 2\left(-23\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-10\right)±\sqrt{100-8\left(-23\right)}}{2\times 2}$$

Whakareatia -8 ki te -23.

$$x=\frac{-\left(-10\right)±\sqrt{100+184}}{2\times 2}$$

Tāpiri 100 ki te 184.

$$x=\frac{-\left(-10\right)±\sqrt{284}}{2\times 2}$$

Tuhia te pūtakerua o te 284.

$$x=\frac{-\left(-10\right)±2\sqrt{71}}{2\times 2}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2\sqrt{71}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{10±2\sqrt{71}}{4}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{71}}{4} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{71}.

$$x=\frac{2\sqrt{71}+10}{4}$$

Whakawehe 10+2\sqrt{71} ki te 4.

$$x=\frac{\sqrt{71}+5}{2}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{71}}{4} ina he tango te ±. Tango 2\sqrt{71} mai i 10.

$$x=\frac{10-2\sqrt{71}}{4}$$

Whakawehe 10-2\sqrt{71} ki te 4.

$$x=\frac{5-\sqrt{71}}{2}$$

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 \frac{5+\sqrt{71}}{2} mō te x_{1} me te \frac{5-\sqrt{71}}{2} mō te x_{2}.

$$2x^{2}-10x-23=2\left(x-\frac{\sqrt{71}+5}{2}\right)\left(x-\frac{5-\sqrt{71}}{2}\right)$$

Aromātai

$$2x^{2}-10x-23$$