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a+b=2 ab=8\left(-3\right)=-24
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 8x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,24 -2,12 -3,8 -4,6
I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -24.
-1+24=23 -2+12=10 -3+8=5 -4+6=2
Tātaihia te tapeke mō ia takirua.
a=-4 b=6
Ko te otinga te takirua ka hoatu i te tapeke 2.
\left(8x^{2}-4x\right)+\left(6x-3\right)
Tuhia anō te 8x^{2}+2x-3 hei \left(8x^{2}-4x\right)+\left(6x-3\right).
4x\left(2x-1\right)+3\left(2x-1\right)
Tauwehea te 4x i te tuatahi me te 3 i te rōpū tuarua.
\left(2x-1\right)\left(4x+3\right)
Whakatauwehea atu te kīanga pātahi 2x-1 mā te whakamahi i te āhuatanga tātai tohatoha.
x=\frac{1}{2} x=-\frac{3}{4}
Hei kimi otinga whārite, me whakaoti te 2x-1=0 me te 4x+3=0.
8x^{2}+2x-3=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{-2±\sqrt{2^{2}-4\times 8\left(-3\right)}}{2\times 8}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 2 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-2±\sqrt{4-4\times 8\left(-3\right)}}{2\times 8}
Pūrua 2.
x=\frac{-2±\sqrt{4-32\left(-3\right)}}{2\times 8}
Whakareatia -4 ki te 8.
x=\frac{-2±\sqrt{4+96}}{2\times 8}
Whakareatia -32 ki te -3.
x=\frac{-2±\sqrt{100}}{2\times 8}
Tāpiri 4 ki te 96.
x=\frac{-2±10}{2\times 8}
Tuhia te pūtakerua o te 100.
x=\frac{-2±10}{16}
Whakareatia 2 ki te 8.
x=\frac{8}{16}
Nā, me whakaoti te whārite x=\frac{-2±10}{16} ina he tāpiri te ±. Tāpiri -2 ki te 10.
x=\frac{1}{2}
Whakahekea te hautanga \frac{8}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.
x=-\frac{12}{16}
Nā, me whakaoti te whārite x=\frac{-2±10}{16} ina he tango te ±. Tango 10 mai i -2.
x=-\frac{3}{4}
Whakahekea te hautanga \frac{-12}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.
x=\frac{1}{2} x=-\frac{3}{4}
Kua oti te whārite te whakatau.
8x^{2}+2x-3=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.
8x^{2}+2x-3-\left(-3\right)=-\left(-3\right)
Me tāpiri 3 ki ngā taha e rua o te whārite.
8x^{2}+2x=-\left(-3\right)
Mā te tango i te -3 i a ia ake anō ka toe ko te 0.
8x^{2}+2x=3
Tango -3 mai i 0.
\frac{8x^{2}+2x}{8}=\frac{3}{8}
Whakawehea ngā taha e rua ki te 8.
x^{2}+\frac{2}{8}x=\frac{3}{8}
Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.
x^{2}+\frac{1}{4}x=\frac{3}{8}
Whakahekea te hautanga \frac{2}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
x^{2}+\frac{1}{4}x+\left(\frac{1}{8}\right)^{2}=\frac{3}{8}+\left(\frac{1}{8}\right)^{2}
Whakawehea te \frac{1}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{8}. Nā, tāpiria te pūrua o te \frac{1}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{3}{8}+\frac{1}{64}
Pūruatia \frac{1}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{25}{64}
Tāpiri \frac{3}{8} ki te \frac{1}{64} 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{1}{8}\right)^{2}=\frac{25}{64}
Tauwehea x^{2}+\frac{1}{4}x+\frac{1}{64}. 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{1}{8}\right)^{2}}=\sqrt{\frac{25}{64}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{1}{8}=\frac{5}{8} x+\frac{1}{8}=-\frac{5}{8}
Whakarūnātia.
x=\frac{1}{2} x=-\frac{3}{4}
Me tango \frac{1}{8} mai i ngā taha e rua o te whārite.