Whakaoti mō x
x = \frac{3 \sqrt{5} - 3}{2} \approx 1.854101966
x=\frac{-3\sqrt{5}-3}{2}\approx -4.854101966
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{2}+3x-9=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{-3±\sqrt{3^{2}-4\left(-9\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 3 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-3±\sqrt{9-4\left(-9\right)}}{2}
Pūrua 3.
x=\frac{-3±\sqrt{9+36}}{2}
Whakareatia -4 ki te -9.
x=\frac{-3±\sqrt{45}}{2}
Tāpiri 9 ki te 36.
x=\frac{-3±3\sqrt{5}}{2}
Tuhia te pūtakerua o te 45.
x=\frac{3\sqrt{5}-3}{2}
Nā, me whakaoti te whārite x=\frac{-3±3\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri -3 ki te 3\sqrt{5}.
x=\frac{-3\sqrt{5}-3}{2}
Nā, me whakaoti te whārite x=\frac{-3±3\sqrt{5}}{2} ina he tango te ±. Tango 3\sqrt{5} mai i -3.
x=\frac{3\sqrt{5}-3}{2} x=\frac{-3\sqrt{5}-3}{2}
Kua oti te whārite te whakatau.
x^{2}+3x-9=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}+3x-9-\left(-9\right)=-\left(-9\right)
Me tāpiri 9 ki ngā taha e rua o te whārite.
x^{2}+3x=-\left(-9\right)
Mā te tango i te -9 i a ia ake anō ka toe ko te 0.
x^{2}+3x=9
Tango -9 mai i 0.
x^{2}+3x+\left(\frac{3}{2}\right)^{2}=9+\left(\frac{3}{2}\right)^{2}
Whakawehea te 3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{2}. Nā, tāpiria te pūrua o te \frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+3x+\frac{9}{4}=9+\frac{9}{4}
Pūruatia \frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+3x+\frac{9}{4}=\frac{45}{4}
Tāpiri 9 ki te \frac{9}{4}.
\left(x+\frac{3}{2}\right)^{2}=\frac{45}{4}
Tauwehea x^{2}+3x+\frac{9}{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+\frac{3}{2}\right)^{2}}=\sqrt{\frac{45}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{3}{2}=\frac{3\sqrt{5}}{2} x+\frac{3}{2}=-\frac{3\sqrt{5}}{2}
Whakarūnātia.
x=\frac{3\sqrt{5}-3}{2} x=\frac{-3\sqrt{5}-3}{2}
Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.
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