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x^{2}+12x-32=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{-12±\sqrt{12^{2}-4\left(-32\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me -32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-12±\sqrt{144-4\left(-32\right)}}{2}
Pūrua 12.
x=\frac{-12±\sqrt{144+128}}{2}
Whakareatia -4 ki te -32.
x=\frac{-12±\sqrt{272}}{2}
Tāpiri 144 ki te 128.
x=\frac{-12±4\sqrt{17}}{2}
Tuhia te pūtakerua o te 272.
x=\frac{4\sqrt{17}-12}{2}
Nā, me whakaoti te whārite x=\frac{-12±4\sqrt{17}}{2} ina he tāpiri te ±. Tāpiri -12 ki te 4\sqrt{17}.
x=2\sqrt{17}-6
Whakawehe -12+4\sqrt{17} ki te 2.
x=\frac{-4\sqrt{17}-12}{2}
Nā, me whakaoti te whārite x=\frac{-12±4\sqrt{17}}{2} ina he tango te ±. Tango 4\sqrt{17} mai i -12.
x=-2\sqrt{17}-6
Whakawehe -12-4\sqrt{17} ki te 2.
x=2\sqrt{17}-6 x=-2\sqrt{17}-6
Kua oti te whārite te whakatau.
x^{2}+12x-32=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}+12x-32-\left(-32\right)=-\left(-32\right)
Me tāpiri 32 ki ngā taha e rua o te whārite.
x^{2}+12x=-\left(-32\right)
Mā te tango i te -32 i a ia ake anō ka toe ko te 0.
x^{2}+12x=32
Tango -32 mai i 0.
x^{2}+12x+6^{2}=32+6^{2}
Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+12x+36=32+36
Pūrua 6.
x^{2}+12x+36=68
Tāpiri 32 ki te 36.
\left(x+6\right)^{2}=68
Tauwehea x^{2}+12x+36. 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+6\right)^{2}}=\sqrt{68}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+6=2\sqrt{17} x+6=-2\sqrt{17}
Whakarūnātia.
x=2\sqrt{17}-6 x=-2\sqrt{17}-6
Me tango 6 mai i ngā taha e rua o te whārite.