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x^{2}+2x-48=0
Whakawehea ngā taha e rua ki te 2.
a+b=2 ab=1\left(-48\right)=-48
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-48. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,48 -2,24 -3,16 -4,12 -6,8
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 -48.
-1+48=47 -2+24=22 -3+16=13 -4+12=8 -6+8=2
Tātaihia te tapeke mō ia takirua.
a=-6 b=8
Ko te otinga te takirua ka hoatu i te tapeke 2.
\left(x^{2}-6x\right)+\left(8x-48\right)
Tuhia anō te x^{2}+2x-48 hei \left(x^{2}-6x\right)+\left(8x-48\right).
x\left(x-6\right)+8\left(x-6\right)
Tauwehea te x i te tuatahi me te 8 i te rōpū tuarua.
\left(x-6\right)\left(x+8\right)
Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.
x=6 x=-8
Hei kimi otinga whārite, me whakaoti te x-6=0 me te x+8=0.
2x^{2}+4x-96=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{-4±\sqrt{4^{2}-4\times 2\left(-96\right)}}{2\times 2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 4 mō b, me -96 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±\sqrt{16-4\times 2\left(-96\right)}}{2\times 2}
Pūrua 4.
x=\frac{-4±\sqrt{16-8\left(-96\right)}}{2\times 2}
Whakareatia -4 ki te 2.
x=\frac{-4±\sqrt{16+768}}{2\times 2}
Whakareatia -8 ki te -96.
x=\frac{-4±\sqrt{784}}{2\times 2}
Tāpiri 16 ki te 768.
x=\frac{-4±28}{2\times 2}
Tuhia te pūtakerua o te 784.
x=\frac{-4±28}{4}
Whakareatia 2 ki te 2.
x=\frac{24}{4}
Nā, me whakaoti te whārite x=\frac{-4±28}{4} ina he tāpiri te ±. Tāpiri -4 ki te 28.
x=6
Whakawehe 24 ki te 4.
x=-\frac{32}{4}
Nā, me whakaoti te whārite x=\frac{-4±28}{4} ina he tango te ±. Tango 28 mai i -4.
x=-8
Whakawehe -32 ki te 4.
x=6 x=-8
Kua oti te whārite te whakatau.
2x^{2}+4x-96=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}+4x-96-\left(-96\right)=-\left(-96\right)
Me tāpiri 96 ki ngā taha e rua o te whārite.
2x^{2}+4x=-\left(-96\right)
Mā te tango i te -96 i a ia ake anō ka toe ko te 0.
2x^{2}+4x=96
Tango -96 mai i 0.
\frac{2x^{2}+4x}{2}=\frac{96}{2}
Whakawehea ngā taha e rua ki te 2.
x^{2}+\frac{4}{2}x=\frac{96}{2}
Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.
x^{2}+2x=\frac{96}{2}
Whakawehe 4 ki te 2.
x^{2}+2x=48
Whakawehe 96 ki te 2.
x^{2}+2x+1^{2}=48+1^{2}
Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+2x+1=48+1
Pūrua 1.
x^{2}+2x+1=49
Tāpiri 48 ki te 1.
\left(x+1\right)^{2}=49
Tauwehea x^{2}+2x+1. 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+1\right)^{2}}=\sqrt{49}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+1=7 x+1=-7
Whakarūnātia.
x=6 x=-8
Me tango 1 mai i ngā taha e rua o te whārite.