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Whakaoti mō x (complex solution)
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Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

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{-2±\sqrt{2^{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{-2±\sqrt{4-4\times 2}}{2}
Pūrua 2.
x=\frac{-2±\sqrt{4-8}}{2}
Whakareatia -4 ki te 2.
x=\frac{-2±\sqrt{-4}}{2}
Tāpiri 4 ki te -8.
x=\frac{-2±2i}{2}
Tuhia te pūtakerua o te -4.
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}=-2+1^{2}
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=-2+1
Pūrua 1.
x^{2}+2x+1=-1
Tāpiri -2 ki te 1.
\left(x+1\right)^{2}=-1
Tauwehea x^{2}+2x+1. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea 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 tango 1 mai i ngā taha e rua o te whārite.