Whakaoti mō x
x=\frac{\sqrt{19}-3}{2}\approx 0.679449472
x=\frac{-\sqrt{19}-3}{2}\approx -3.679449472
Graph
Tohaina
Kua tāruatia ki te papatopenga
2x^{2}+6x-5=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{-6±\sqrt{6^{2}-4\times 2\left(-5\right)}}{2\times 2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 6 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-6±\sqrt{36-4\times 2\left(-5\right)}}{2\times 2}
Pūrua 6.
x=\frac{-6±\sqrt{36-8\left(-5\right)}}{2\times 2}
Whakareatia -4 ki te 2.
x=\frac{-6±\sqrt{36+40}}{2\times 2}
Whakareatia -8 ki te -5.
x=\frac{-6±\sqrt{76}}{2\times 2}
Tāpiri 36 ki te 40.
x=\frac{-6±2\sqrt{19}}{2\times 2}
Tuhia te pūtakerua o te 76.
x=\frac{-6±2\sqrt{19}}{4}
Whakareatia 2 ki te 2.
x=\frac{2\sqrt{19}-6}{4}
Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{19}}{4} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{19}.
x=\frac{\sqrt{19}-3}{2}
Whakawehe -6+2\sqrt{19} ki te 4.
x=\frac{-2\sqrt{19}-6}{4}
Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{19}}{4} ina he tango te ±. Tango 2\sqrt{19} mai i -6.
x=\frac{-\sqrt{19}-3}{2}
Whakawehe -6-2\sqrt{19} ki te 4.
x=\frac{\sqrt{19}-3}{2} x=\frac{-\sqrt{19}-3}{2}
Kua oti te whārite te whakatau.
2x^{2}+6x-5=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.
2x^{2}+6x-5-\left(-5\right)=-\left(-5\right)
Me tāpiri 5 ki ngā taha e rua o te whārite.
2x^{2}+6x=-\left(-5\right)
Mā te tango i te -5 i a ia ake anō ka toe ko te 0.
2x^{2}+6x=5
Tango -5 mai i 0.
\frac{2x^{2}+6x}{2}=\frac{5}{2}
Whakawehea ngā taha e rua ki te 2.
x^{2}+\frac{6}{2}x=\frac{5}{2}
Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.
x^{2}+3x=\frac{5}{2}
Whakawehe 6 ki te 2.
x^{2}+3x+\left(\frac{3}{2}\right)^{2}=\frac{5}{2}+\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}=\frac{5}{2}+\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{19}{4}
Tāpiri \frac{5}{2} ki te \frac{9}{4} 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{3}{2}\right)^{2}=\frac{19}{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{19}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{3}{2}=\frac{\sqrt{19}}{2} x+\frac{3}{2}=-\frac{\sqrt{19}}{2}
Whakarūnātia.
x=\frac{\sqrt{19}-3}{2} x=\frac{-\sqrt{19}-3}{2}
Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.
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