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6x^{2}+12x-5x=-2
Tangohia te 5x mai i ngā taha e rua.
6x^{2}+7x=-2
Pahekotia te 12x me -5x, ka 7x.
6x^{2}+7x+2=0
Me tāpiri te 2 ki ngā taha e rua.
a+b=7 ab=6\times 2=12
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 6x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,12 2,6 3,4
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.
1+12=13 2+6=8 3+4=7
Tātaihia te tapeke mō ia takirua.
a=3 b=4
Ko te otinga te takirua ka hoatu i te tapeke 7.
\left(6x^{2}+3x\right)+\left(4x+2\right)
Tuhia anō te 6x^{2}+7x+2 hei \left(6x^{2}+3x\right)+\left(4x+2\right).
3x\left(2x+1\right)+2\left(2x+1\right)
Tauwehea te 3x i te tuatahi me te 2 i te rōpū tuarua.
\left(2x+1\right)\left(3x+2\right)
Whakatauwehea atu te kīanga pātahi 2x+1 mā te whakamahi i te āhuatanga tātai tohatoha.
x=-\frac{1}{2} x=-\frac{2}{3}
Hei kimi otinga whārite, me whakaoti te 2x+1=0 me te 3x+2=0.
6x^{2}+12x-5x=-2
Tangohia te 5x mai i ngā taha e rua.
6x^{2}+7x=-2
Pahekotia te 12x me -5x, ka 7x.
6x^{2}+7x+2=0
Me tāpiri te 2 ki ngā taha e rua.
x=\frac{-7±\sqrt{7^{2}-4\times 6\times 2}}{2\times 6}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 7 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-7±\sqrt{49-4\times 6\times 2}}{2\times 6}
Pūrua 7.
x=\frac{-7±\sqrt{49-24\times 2}}{2\times 6}
Whakareatia -4 ki te 6.
x=\frac{-7±\sqrt{49-48}}{2\times 6}
Whakareatia -24 ki te 2.
x=\frac{-7±\sqrt{1}}{2\times 6}
Tāpiri 49 ki te -48.
x=\frac{-7±1}{2\times 6}
Tuhia te pūtakerua o te 1.
x=\frac{-7±1}{12}
Whakareatia 2 ki te 6.
x=-\frac{6}{12}
Nā, me whakaoti te whārite x=\frac{-7±1}{12} ina he tāpiri te ±. Tāpiri -7 ki te 1.
x=-\frac{1}{2}
Whakahekea te hautanga \frac{-6}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.
x=-\frac{8}{12}
Nā, me whakaoti te whārite x=\frac{-7±1}{12} ina he tango te ±. Tango 1 mai i -7.
x=-\frac{2}{3}
Whakahekea te hautanga \frac{-8}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.
x=-\frac{1}{2} x=-\frac{2}{3}
Kua oti te whārite te whakatau.
6x^{2}+12x-5x=-2
Tangohia te 5x mai i ngā taha e rua.
6x^{2}+7x=-2
Pahekotia te 12x me -5x, ka 7x.
\frac{6x^{2}+7x}{6}=-\frac{2}{6}
Whakawehea ngā taha e rua ki te 6.
x^{2}+\frac{7}{6}x=-\frac{2}{6}
Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.
x^{2}+\frac{7}{6}x=-\frac{1}{3}
Whakahekea te hautanga \frac{-2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
x^{2}+\frac{7}{6}x+\left(\frac{7}{12}\right)^{2}=-\frac{1}{3}+\left(\frac{7}{12}\right)^{2}
Whakawehea te \frac{7}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{12}. Nā, tāpiria te pūrua o te \frac{7}{12} 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}{6}x+\frac{49}{144}=-\frac{1}{3}+\frac{49}{144}
Pūruatia \frac{7}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+\frac{7}{6}x+\frac{49}{144}=\frac{1}{144}
Tāpiri -\frac{1}{3} ki te \frac{49}{144} 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}{12}\right)^{2}=\frac{1}{144}
Tauwehea x^{2}+\frac{7}{6}x+\frac{49}{144}. 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}{12}\right)^{2}}=\sqrt{\frac{1}{144}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{7}{12}=\frac{1}{12} x+\frac{7}{12}=-\frac{1}{12}
Whakarūnātia.
x=-\frac{1}{2} x=-\frac{2}{3}
Me tango \frac{7}{12} mai i ngā taha e rua o te whārite.