Whakaoti mō x
x=3\sqrt{5}\approx 6.708203932
x=-3\sqrt{5}\approx -6.708203932
Graph
Tohaina
Kua tāruatia ki te papatopenga
3\times 75=3xx+\frac{2}{3}x\times 3x
Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.
225=3xx+\frac{2}{3}x\times 3x
Whakareatia te 3 ki te 75, ka 225.
225=3x^{2}+\frac{2}{3}x\times 3x
Whakareatia te x ki te x, ka x^{2}.
225=3x^{2}+\frac{2}{3}x^{2}\times 3
Whakareatia te x ki te x, ka x^{2}.
225=3x^{2}+2x^{2}
Me whakakore te 3 me te 3.
225=5x^{2}
Pahekotia te 3x^{2} me 2x^{2}, ka 5x^{2}.
5x^{2}=225
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
x^{2}=\frac{225}{5}
Whakawehea ngā taha e rua ki te 5.
x^{2}=45
Whakawehea te 225 ki te 5, kia riro ko 45.
x=3\sqrt{5} x=-3\sqrt{5}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
3\times 75=3xx+\frac{2}{3}x\times 3x
Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.
225=3xx+\frac{2}{3}x\times 3x
Whakareatia te 3 ki te 75, ka 225.
225=3x^{2}+\frac{2}{3}x\times 3x
Whakareatia te x ki te x, ka x^{2}.
225=3x^{2}+\frac{2}{3}x^{2}\times 3
Whakareatia te x ki te x, ka x^{2}.
225=3x^{2}+2x^{2}
Me whakakore te 3 me te 3.
225=5x^{2}
Pahekotia te 3x^{2} me 2x^{2}, ka 5x^{2}.
5x^{2}=225
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
5x^{2}-225=0
Tangohia te 225 mai i ngā taha e rua.
x=\frac{0±\sqrt{0^{2}-4\times 5\left(-225\right)}}{2\times 5}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -225 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 5\left(-225\right)}}{2\times 5}
Pūrua 0.
x=\frac{0±\sqrt{-20\left(-225\right)}}{2\times 5}
Whakareatia -4 ki te 5.
x=\frac{0±\sqrt{4500}}{2\times 5}
Whakareatia -20 ki te -225.
x=\frac{0±30\sqrt{5}}{2\times 5}
Tuhia te pūtakerua o te 4500.
x=\frac{0±30\sqrt{5}}{10}
Whakareatia 2 ki te 5.
x=3\sqrt{5}
Nā, me whakaoti te whārite x=\frac{0±30\sqrt{5}}{10} ina he tāpiri te ±.
x=-3\sqrt{5}
Nā, me whakaoti te whārite x=\frac{0±30\sqrt{5}}{10} ina he tango te ±.
x=3\sqrt{5} x=-3\sqrt{5}
Kua oti te whārite te whakatau.
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