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Whakaoti mō x (complex solution)
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Whakaoti mō x
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x^{2}+54x-5=500
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^{2}+54x-5-500=500-500
Me tango 500 mai i ngā taha e rua o te whārite.
x^{2}+54x-5-500=0
Mā te tango i te 500 i a ia ake anō ka toe ko te 0.
x^{2}+54x-505=0
Tango 500 mai i -5.
x=\frac{-54±\sqrt{54^{2}-4\left(-505\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 54 mō b, me -505 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-54±\sqrt{2916-4\left(-505\right)}}{2}
Pūrua 54.
x=\frac{-54±\sqrt{2916+2020}}{2}
Whakareatia -4 ki te -505.
x=\frac{-54±\sqrt{4936}}{2}
Tāpiri 2916 ki te 2020.
x=\frac{-54±2\sqrt{1234}}{2}
Tuhia te pūtakerua o te 4936.
x=\frac{2\sqrt{1234}-54}{2}
Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tāpiri te ±. Tāpiri -54 ki te 2\sqrt{1234}.
x=\sqrt{1234}-27
Whakawehe -54+2\sqrt{1234} ki te 2.
x=\frac{-2\sqrt{1234}-54}{2}
Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tango te ±. Tango 2\sqrt{1234} mai i -54.
x=-\sqrt{1234}-27
Whakawehe -54-2\sqrt{1234} ki te 2.
x=\sqrt{1234}-27 x=-\sqrt{1234}-27
Kua oti te whārite te whakatau.
x^{2}+54x-5=500
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}+54x-5-\left(-5\right)=500-\left(-5\right)
Me tāpiri 5 ki ngā taha e rua o te whārite.
x^{2}+54x=500-\left(-5\right)
Mā te tango i te -5 i a ia ake anō ka toe ko te 0.
x^{2}+54x=505
Tango -5 mai i 500.
x^{2}+54x+27^{2}=505+27^{2}
Whakawehea te 54, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 27. Nā, tāpiria te pūrua o te 27 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+54x+729=505+729
Pūrua 27.
x^{2}+54x+729=1234
Tāpiri 505 ki te 729.
\left(x+27\right)^{2}=1234
Tauwehea x^{2}+54x+729. 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+27\right)^{2}}=\sqrt{1234}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+27=\sqrt{1234} x+27=-\sqrt{1234}
Whakarūnātia.
x=\sqrt{1234}-27 x=-\sqrt{1234}-27
Me tango 27 mai i ngā taha e rua o te whārite.
x^{2}+54x-5=500
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^{2}+54x-5-500=500-500
Me tango 500 mai i ngā taha e rua o te whārite.
x^{2}+54x-5-500=0
Mā te tango i te 500 i a ia ake anō ka toe ko te 0.
x^{2}+54x-505=0
Tango 500 mai i -5.
x=\frac{-54±\sqrt{54^{2}-4\left(-505\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 54 mō b, me -505 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-54±\sqrt{2916-4\left(-505\right)}}{2}
Pūrua 54.
x=\frac{-54±\sqrt{2916+2020}}{2}
Whakareatia -4 ki te -505.
x=\frac{-54±\sqrt{4936}}{2}
Tāpiri 2916 ki te 2020.
x=\frac{-54±2\sqrt{1234}}{2}
Tuhia te pūtakerua o te 4936.
x=\frac{2\sqrt{1234}-54}{2}
Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tāpiri te ±. Tāpiri -54 ki te 2\sqrt{1234}.
x=\sqrt{1234}-27
Whakawehe -54+2\sqrt{1234} ki te 2.
x=\frac{-2\sqrt{1234}-54}{2}
Nā, me whakaoti te whārite x=\frac{-54±2\sqrt{1234}}{2} ina he tango te ±. Tango 2\sqrt{1234} mai i -54.
x=-\sqrt{1234}-27
Whakawehe -54-2\sqrt{1234} ki te 2.
x=\sqrt{1234}-27 x=-\sqrt{1234}-27
Kua oti te whārite te whakatau.
x^{2}+54x-5=500
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}+54x-5-\left(-5\right)=500-\left(-5\right)
Me tāpiri 5 ki ngā taha e rua o te whārite.
x^{2}+54x=500-\left(-5\right)
Mā te tango i te -5 i a ia ake anō ka toe ko te 0.
x^{2}+54x=505
Tango -5 mai i 500.
x^{2}+54x+27^{2}=505+27^{2}
Whakawehea te 54, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 27. Nā, tāpiria te pūrua o te 27 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+54x+729=505+729
Pūrua 27.
x^{2}+54x+729=1234
Tāpiri 505 ki te 729.
\left(x+27\right)^{2}=1234
Tauwehea x^{2}+54x+729. 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+27\right)^{2}}=\sqrt{1234}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+27=\sqrt{1234} x+27=-\sqrt{1234}
Whakarūnātia.
x=\sqrt{1234}-27 x=-\sqrt{1234}-27
Me tango 27 mai i ngā taha e rua o te whārite.