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Whakaoti mō x (complex solution)
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Whakaoti mō x
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x^{2}+8x+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{-8±\sqrt{8^{2}-4\times 2}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-8±\sqrt{64-4\times 2}}{2}
Pūrua 8.
x=\frac{-8±\sqrt{64-8}}{2}
Whakareatia -4 ki te 2.
x=\frac{-8±\sqrt{56}}{2}
Tāpiri 64 ki te -8.
x=\frac{-8±2\sqrt{14}}{2}
Tuhia te pūtakerua o te 56.
x=\frac{2\sqrt{14}-8}{2}
Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{14}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{14}.
x=\sqrt{14}-4
Whakawehe -8+2\sqrt{14} ki te 2.
x=\frac{-2\sqrt{14}-8}{2}
Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{14}}{2} ina he tango te ±. Tango 2\sqrt{14} mai i -8.
x=-\sqrt{14}-4
Whakawehe -8-2\sqrt{14} ki te 2.
x=\sqrt{14}-4 x=-\sqrt{14}-4
Kua oti te whārite te whakatau.
x^{2}+8x+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}+8x+2-2=-2
Me tango 2 mai i ngā taha e rua o te whārite.
x^{2}+8x=-2
Mā te tango i te 2 i a ia ake anō ka toe ko te 0.
x^{2}+8x+4^{2}=-2+4^{2}
Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+8x+16=-2+16
Pūrua 4.
x^{2}+8x+16=14
Tāpiri -2 ki te 16.
\left(x+4\right)^{2}=14
Tauwehea te x^{2}+8x+16. 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+4\right)^{2}}=\sqrt{14}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+4=\sqrt{14} x+4=-\sqrt{14}
Whakarūnātia.
x=\sqrt{14}-4 x=-\sqrt{14}-4
Me tango 4 mai i ngā taha e rua o te whārite.
x^{2}+8x+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{-8±\sqrt{8^{2}-4\times 2}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-8±\sqrt{64-4\times 2}}{2}
Pūrua 8.
x=\frac{-8±\sqrt{64-8}}{2}
Whakareatia -4 ki te 2.
x=\frac{-8±\sqrt{56}}{2}
Tāpiri 64 ki te -8.
x=\frac{-8±2\sqrt{14}}{2}
Tuhia te pūtakerua o te 56.
x=\frac{2\sqrt{14}-8}{2}
Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{14}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{14}.
x=\sqrt{14}-4
Whakawehe -8+2\sqrt{14} ki te 2.
x=\frac{-2\sqrt{14}-8}{2}
Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{14}}{2} ina he tango te ±. Tango 2\sqrt{14} mai i -8.
x=-\sqrt{14}-4
Whakawehe -8-2\sqrt{14} ki te 2.
x=\sqrt{14}-4 x=-\sqrt{14}-4
Kua oti te whārite te whakatau.
x^{2}+8x+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}+8x+2-2=-2
Me tango 2 mai i ngā taha e rua o te whārite.
x^{2}+8x=-2
Mā te tango i te 2 i a ia ake anō ka toe ko te 0.
x^{2}+8x+4^{2}=-2+4^{2}
Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+8x+16=-2+16
Pūrua 4.
x^{2}+8x+16=14
Tāpiri -2 ki te 16.
\left(x+4\right)^{2}=14
Tauwehea te x^{2}+8x+16. 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+4\right)^{2}}=\sqrt{14}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+4=\sqrt{14} x+4=-\sqrt{14}
Whakarūnātia.
x=\sqrt{14}-4 x=-\sqrt{14}-4
Me tango 4 mai i ngā taha e rua o te whārite.