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5\left(3x^{2}+x\right)
Tauwehea te 5.
x\left(3x+1\right)
Whakaarohia te 3x^{2}+x. Tauwehea te x.
5x\left(3x+1\right)
Me tuhi anō te kīanga whakatauwehe katoa.
15x^{2}+5x=0
Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.
x=\frac{-5±\sqrt{5^{2}}}{2\times 15}
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{-5±5}{2\times 15}
Tuhia te pūtakerua o te 5^{2}.
x=\frac{-5±5}{30}
Whakareatia 2 ki te 15.
x=\frac{0}{30}
Nā, me whakaoti te whārite x=\frac{-5±5}{30} ina he tāpiri te ±. Tāpiri -5 ki te 5.
x=0
Whakawehe 0 ki te 30.
x=-\frac{10}{30}
Nā, me whakaoti te whārite x=\frac{-5±5}{30} ina he tango te ±. Tango 5 mai i -5.
x=-\frac{1}{3}
Whakahekea te hautanga \frac{-10}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.
15x^{2}+5x=15x\left(x-\left(-\frac{1}{3}\right)\right)
Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 0 mō te x_{1} me te -\frac{1}{3} mō te x_{2}.
15x^{2}+5x=15x\left(x+\frac{1}{3}\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.
15x^{2}+5x=15x\times \frac{3x+1}{3}
Tāpiri \frac{1}{3} ki te x 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.
15x^{2}+5x=5x\left(3x+1\right)
Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 15 me te 3.