Whakaoti mō x
x=\frac{\sqrt{145}-7}{6}\approx 0.840265763
x=\frac{-\sqrt{145}-7}{6}\approx -3.173599096
Graph
Tohaina
Kua tāruatia ki te papatopenga
3x^{2}+7x-8=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{-7±\sqrt{7^{2}-4\times 3\left(-8\right)}}{2\times 3}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 7 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-7±\sqrt{49-4\times 3\left(-8\right)}}{2\times 3}
Pūrua 7.
x=\frac{-7±\sqrt{49-12\left(-8\right)}}{2\times 3}
Whakareatia -4 ki te 3.
x=\frac{-7±\sqrt{49+96}}{2\times 3}
Whakareatia -12 ki te -8.
x=\frac{-7±\sqrt{145}}{2\times 3}
Tāpiri 49 ki te 96.
x=\frac{-7±\sqrt{145}}{6}
Whakareatia 2 ki te 3.
x=\frac{\sqrt{145}-7}{6}
Nā, me whakaoti te whārite x=\frac{-7±\sqrt{145}}{6} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{145}.
x=\frac{-\sqrt{145}-7}{6}
Nā, me whakaoti te whārite x=\frac{-7±\sqrt{145}}{6} ina he tango te ±. Tango \sqrt{145} mai i -7.
x=\frac{\sqrt{145}-7}{6} x=\frac{-\sqrt{145}-7}{6}
Kua oti te whārite te whakatau.
3x^{2}+7x-8=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.
3x^{2}+7x-8-\left(-8\right)=-\left(-8\right)
Me tāpiri 8 ki ngā taha e rua o te whārite.
3x^{2}+7x=-\left(-8\right)
Mā te tango i te -8 i a ia ake anō ka toe ko te 0.
3x^{2}+7x=8
Tango -8 mai i 0.
\frac{3x^{2}+7x}{3}=\frac{8}{3}
Whakawehea ngā taha e rua ki te 3.
x^{2}+\frac{7}{3}x=\frac{8}{3}
Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.
x^{2}+\frac{7}{3}x+\left(\frac{7}{6}\right)^{2}=\frac{8}{3}+\left(\frac{7}{6}\right)^{2}
Whakawehea te \frac{7}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{6}. Nā, tāpiria te pūrua o te \frac{7}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+\frac{7}{3}x+\frac{49}{36}=\frac{8}{3}+\frac{49}{36}
Pūruatia \frac{7}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+\frac{7}{3}x+\frac{49}{36}=\frac{145}{36}
Tāpiri \frac{8}{3} ki te \frac{49}{36} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
\left(x+\frac{7}{6}\right)^{2}=\frac{145}{36}
Tauwehea x^{2}+\frac{7}{3}x+\frac{49}{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+\frac{7}{6}\right)^{2}}=\sqrt{\frac{145}{36}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{7}{6}=\frac{\sqrt{145}}{6} x+\frac{7}{6}=-\frac{\sqrt{145}}{6}
Whakarūnātia.
x=\frac{\sqrt{145}-7}{6} x=\frac{-\sqrt{145}-7}{6}
Me tango \frac{7}{6} mai i ngā taha e rua o te whārite.
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