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-2x^{2}+8x+4=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{-8±\sqrt{8^{2}-4\left(-2\right)\times 4}}{2\left(-2\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{-8±\sqrt{64-4\left(-2\right)\times 4}}{2\left(-2\right)}
Pūrua 8.
x=\frac{-8±\sqrt{64+8\times 4}}{2\left(-2\right)}
Whakareatia -4 ki te -2.
x=\frac{-8±\sqrt{64+32}}{2\left(-2\right)}
Whakareatia 8 ki te 4.
x=\frac{-8±\sqrt{96}}{2\left(-2\right)}
Tāpiri 64 ki te 32.
x=\frac{-8±4\sqrt{6}}{2\left(-2\right)}
Tuhia te pūtakerua o te 96.
x=\frac{-8±4\sqrt{6}}{-4}
Whakareatia 2 ki te -2.
x=\frac{4\sqrt{6}-8}{-4}
Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{6}}{-4} ina he tāpiri te ±. Tāpiri -8 ki te 4\sqrt{6}.
x=2-\sqrt{6}
Whakawehe -8+4\sqrt{6} ki te -4.
x=\frac{-4\sqrt{6}-8}{-4}
Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{6}}{-4} ina he tango te ±. Tango 4\sqrt{6} mai i -8.
x=\sqrt{6}+2
Whakawehe -8-4\sqrt{6} ki te -4.
-2x^{2}+8x+4=-2\left(x-\left(2-\sqrt{6}\right)\right)\left(x-\left(\sqrt{6}+2\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 2-\sqrt{6} mō te x_{1} me te 2+\sqrt{6} mō te x_{2}.