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n^{2}+2n-1=6
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.
n^{2}+2n-1-6=6-6
Me tango 6 mai i ngā taha e rua o te whārite.
n^{2}+2n-1-6=0
Mā te tango i te 6 i a ia ake anō ka toe ko te 0.
n^{2}+2n-7=0
Tango 6 mai i -1.
n=\frac{-2±\sqrt{2^{2}-4\left(-7\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
n=\frac{-2±\sqrt{4-4\left(-7\right)}}{2}
Pūrua 2.
n=\frac{-2±\sqrt{4+28}}{2}
Whakareatia -4 ki te -7.
n=\frac{-2±\sqrt{32}}{2}
Tāpiri 4 ki te 28.
n=\frac{-2±4\sqrt{2}}{2}
Tuhia te pūtakerua o te 32.
n=\frac{4\sqrt{2}-2}{2}
Nā, me whakaoti te whārite n=\frac{-2±4\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri -2 ki te 4\sqrt{2}.
n=2\sqrt{2}-1
Whakawehe 4\sqrt{2}-2 ki te 2.
n=\frac{-4\sqrt{2}-2}{2}
Nā, me whakaoti te whārite n=\frac{-2±4\sqrt{2}}{2} ina he tango te ±. Tango 4\sqrt{2} mai i -2.
n=-2\sqrt{2}-1
Whakawehe -2-4\sqrt{2} ki te 2.
n=2\sqrt{2}-1 n=-2\sqrt{2}-1
Kua oti te whārite te whakatau.
n^{2}+2n-1=6
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.
n^{2}+2n-1-\left(-1\right)=6-\left(-1\right)
Me tāpiri 1 ki ngā taha e rua o te whārite.
n^{2}+2n=6-\left(-1\right)
Mā te tango i te -1 i a ia ake anō ka toe ko te 0.
n^{2}+2n=7
Tango -1 mai i 6.
n^{2}+2n+1^{2}=7+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.
n^{2}+2n+1=7+1
Pūrua 1.
n^{2}+2n+1=8
Tāpiri 7 ki te 1.
\left(n+1\right)^{2}=8
Tauwehea te n^{2}+2n+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(n+1\right)^{2}}=\sqrt{8}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
n+1=2\sqrt{2} n+1=-2\sqrt{2}
Whakarūnātia.
n=2\sqrt{2}-1 n=-2\sqrt{2}-1
Me tango 1 mai i ngā taha e rua o te whārite.