Whakaoti i te x^2-25x-35

$${ x }^{ 2 } -25x-35$$

Tauwehe

$$\left(x-\frac{25-3\sqrt{85}}{2}\right)\left(x-\frac{3\sqrt{85}+25}{2}\right)$$

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.

$$x^{2}-25x-35=0$$

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.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}-4\left(-35\right)}}{2}$$

Pūrua -25.

$$x=\frac{-\left(-25\right)±\sqrt{625-4\left(-35\right)}}{2}$$

Whakareatia -4 ki te -35.

$$x=\frac{-\left(-25\right)±\sqrt{625+140}}{2}$$

Tāpiri 625 ki te 140.

$$x=\frac{-\left(-25\right)±\sqrt{765}}{2}$$

Tuhia te pūtakerua o te 765.

$$x=\frac{-\left(-25\right)±3\sqrt{85}}{2}$$

Ko te tauaro o -25 ko 25.

$$x=\frac{25±3\sqrt{85}}{2}$$

Nā, me whakaoti te whārite x=\frac{25±3\sqrt{85}}{2} ina he tāpiri te ±. Tāpiri 25 ki te 3\sqrt{85}.

$$x=\frac{3\sqrt{85}+25}{2}$$

Nā, me whakaoti te whārite x=\frac{25±3\sqrt{85}}{2} ina he tango te ±. Tango 3\sqrt{85} mai i 25.

$$x=\frac{25-3\sqrt{85}}{2}$$

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{25+3\sqrt{85}}{2} mō te x_{1} me te \frac{25-3\sqrt{85}}{2} mō te x_{2}.

$$x^{2}-25x-35=\left(x-\frac{3\sqrt{85}+25}{2}\right)\left(x-\frac{25-3\sqrt{85}}{2}\right)$$

Aromātai

$$x^{2}-25x-35$$