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x^{2}-5x+5=0
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=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 5}}{2}
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(-5\right)±\sqrt{25-4\times 5}}{2}
Pūrua -5.
x=\frac{-\left(-5\right)±\sqrt{25-20}}{2}
Whakareatia -4 ki te 5.
x=\frac{-\left(-5\right)±\sqrt{5}}{2}
Tāpiri 25 ki te -20.
x=\frac{5±\sqrt{5}}{2}
Ko te tauaro o -5 ko 5.
x=\frac{\sqrt{5}+5}{2}
Nā, me whakaoti te whārite x=\frac{5±\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{5}.
x=\frac{5-\sqrt{5}}{2}
Nā, me whakaoti te whārite x=\frac{5±\sqrt{5}}{2} ina he tango te ±. Tango \sqrt{5} mai i 5.
x^{2}-5x+5=\left(x-\frac{\sqrt{5}+5}{2}\right)\left(x-\frac{5-\sqrt{5}}{2}\right)
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{5}}{2} mō te x_{1} me te \frac{5-\sqrt{5}}{2} mō te x_{2}.