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Whakaoti mō x (complex solution)
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x^{2}-2x+2=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(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±\sqrt{4-4\times 2}}{2}
Pūrua -2.
x=\frac{-\left(-2\right)±\sqrt{4-8}}{2}
Whakareatia -4 ki te 2.
x=\frac{-\left(-2\right)±\sqrt{-4}}{2}
Tāpiri 4 ki te -8.
x=\frac{-\left(-2\right)±2i}{2}
Tuhia te pūtakerua o te -4.
x=\frac{2±2i}{2}
Ko te tauaro o -2 ko 2.
x=\frac{2+2i}{2}
Nā, me whakaoti te whārite x=\frac{2±2i}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2i.
x=1+i
Whakawehe 2+2i ki te 2.
x=\frac{2-2i}{2}
Nā, me whakaoti te whārite x=\frac{2±2i}{2} ina he tango te ±. Tango 2i mai i 2.
x=1-i
Whakawehe 2-2i ki te 2.
x=1+i x=1-i
Kua oti te whārite te whakatau.
x^{2}-2x+2=0
Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.
x^{2}-2x+2-2=-2
Me tango 2 mai i ngā taha e rua o te whārite.
x^{2}-2x=-2
Mā te tango i te 2 i a ia ake anō ka toe ko te 0.
x^{2}-2x+1=-2+1
Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-2x+1=-1
Tāpiri -2 ki te 1.
\left(x-1\right)^{2}=-1
Tauwehea te x^{2}-2x+1. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-1\right)^{2}}=\sqrt{-1}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-1=i x-1=-i
Whakarūnātia.
x=1+i x=1-i
Me tāpiri 1 ki ngā taha e rua o te whārite.