Whakaoti mō x (complex solution)
x=\sqrt{19}-2\approx 2.358898944
x=-\left(\sqrt{19}+2\right)\approx -6.358898944
Whakaoti mō x
x=\sqrt{19}-2\approx 2.358898944
x=-\sqrt{19}-2\approx -6.358898944
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{2}+4x-3=12
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}+4x-3-12=12-12
Me tango 12 mai i ngā taha e rua o te whārite.
x^{2}+4x-3-12=0
Mā te tango i te 12 i a ia ake anō ka toe ko te 0.
x^{2}+4x-15=0
Tango 12 mai i -3.
x=\frac{-4±\sqrt{4^{2}-4\left(-15\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±\sqrt{16-4\left(-15\right)}}{2}
Pūrua 4.
x=\frac{-4±\sqrt{16+60}}{2}
Whakareatia -4 ki te -15.
x=\frac{-4±\sqrt{76}}{2}
Tāpiri 16 ki te 60.
x=\frac{-4±2\sqrt{19}}{2}
Tuhia te pūtakerua o te 76.
x=\frac{2\sqrt{19}-4}{2}
Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{19}}{2} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{19}.
x=\sqrt{19}-2
Whakawehe -4+2\sqrt{19} ki te 2.
x=\frac{-2\sqrt{19}-4}{2}
Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{19}}{2} ina he tango te ±. Tango 2\sqrt{19} mai i -4.
x=-\sqrt{19}-2
Whakawehe -4-2\sqrt{19} ki te 2.
x=\sqrt{19}-2 x=-\sqrt{19}-2
Kua oti te whārite te whakatau.
x^{2}+4x-3=12
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}+4x-3-\left(-3\right)=12-\left(-3\right)
Me tāpiri 3 ki ngā taha e rua o te whārite.
x^{2}+4x=12-\left(-3\right)
Mā te tango i te -3 i a ia ake anō ka toe ko te 0.
x^{2}+4x=15
Tango -3 mai i 12.
x^{2}+4x+2^{2}=15+2^{2}
Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+4x+4=15+4
Pūrua 2.
x^{2}+4x+4=19
Tāpiri 15 ki te 4.
\left(x+2\right)^{2}=19
Tauwehea x^{2}+4x+4. 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+2\right)^{2}}=\sqrt{19}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+2=\sqrt{19} x+2=-\sqrt{19}
Whakarūnātia.
x=\sqrt{19}-2 x=-\sqrt{19}-2
Me tango 2 mai i ngā taha e rua o te whārite.
x^{2}+4x-3=12
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}+4x-3-12=12-12
Me tango 12 mai i ngā taha e rua o te whārite.
x^{2}+4x-3-12=0
Mā te tango i te 12 i a ia ake anō ka toe ko te 0.
x^{2}+4x-15=0
Tango 12 mai i -3.
x=\frac{-4±\sqrt{4^{2}-4\left(-15\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±\sqrt{16-4\left(-15\right)}}{2}
Pūrua 4.
x=\frac{-4±\sqrt{16+60}}{2}
Whakareatia -4 ki te -15.
x=\frac{-4±\sqrt{76}}{2}
Tāpiri 16 ki te 60.
x=\frac{-4±2\sqrt{19}}{2}
Tuhia te pūtakerua o te 76.
x=\frac{2\sqrt{19}-4}{2}
Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{19}}{2} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{19}.
x=\sqrt{19}-2
Whakawehe -4+2\sqrt{19} ki te 2.
x=\frac{-2\sqrt{19}-4}{2}
Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{19}}{2} ina he tango te ±. Tango 2\sqrt{19} mai i -4.
x=-\sqrt{19}-2
Whakawehe -4-2\sqrt{19} ki te 2.
x=\sqrt{19}-2 x=-\sqrt{19}-2
Kua oti te whārite te whakatau.
x^{2}+4x-3=12
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}+4x-3-\left(-3\right)=12-\left(-3\right)
Me tāpiri 3 ki ngā taha e rua o te whārite.
x^{2}+4x=12-\left(-3\right)
Mā te tango i te -3 i a ia ake anō ka toe ko te 0.
x^{2}+4x=15
Tango -3 mai i 12.
x^{2}+4x+2^{2}=15+2^{2}
Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+4x+4=15+4
Pūrua 2.
x^{2}+4x+4=19
Tāpiri 15 ki te 4.
\left(x+2\right)^{2}=19
Tauwehea x^{2}+4x+4. 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+2\right)^{2}}=\sqrt{19}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+2=\sqrt{19} x+2=-\sqrt{19}
Whakarūnātia.
x=\sqrt{19}-2 x=-\sqrt{19}-2
Me tango 2 mai i ngā taha e rua o te whārite.
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