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-x^{2}+6x+2=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{-6±\sqrt{6^{2}-4\left(-1\right)\times 2}}{2\left(-1\right)}
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{-6±\sqrt{36-4\left(-1\right)\times 2}}{2\left(-1\right)}
Pūrua 6.
x=\frac{-6±\sqrt{36+4\times 2}}{2\left(-1\right)}
Whakareatia -4 ki te -1.
x=\frac{-6±\sqrt{36+8}}{2\left(-1\right)}
Whakareatia 4 ki te 2.
x=\frac{-6±\sqrt{44}}{2\left(-1\right)}
Tāpiri 36 ki te 8.
x=\frac{-6±2\sqrt{11}}{2\left(-1\right)}
Tuhia te pūtakerua o te 44.
x=\frac{-6±2\sqrt{11}}{-2}
Whakareatia 2 ki te -1.
x=\frac{2\sqrt{11}-6}{-2}
Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{11}}{-2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{11}.
x=3-\sqrt{11}
Whakawehe -6+2\sqrt{11} ki te -2.
x=\frac{-2\sqrt{11}-6}{-2}
Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{11}}{-2} ina he tango te ±. Tango 2\sqrt{11} mai i -6.
x=\sqrt{11}+3
Whakawehe -6-2\sqrt{11} ki te -2.
-x^{2}+6x+2=-\left(x-\left(3-\sqrt{11}\right)\right)\left(x-\left(\sqrt{11}+3\right)\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 3-\sqrt{11} mō te x_{1} me te 3+\sqrt{11} mō te x_{2}.