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x^{2}+x-48-3x=0
Tangohia te 3x mai i ngā taha e rua.
x^{2}-2x-48=0
Pahekotia te x me -3x, ka -2x.
a+b=-2 ab=-48
Hei whakaoti i te whārite, whakatauwehea te x^{2}-2x-48 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). 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 tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. 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=-8 b=6
Ko te otinga te takirua ka hoatu i te tapeke -2.
\left(x-8\right)\left(x+6\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=8 x=-6
Hei kimi otinga whārite, me whakaoti te x-8=0 me te x+6=0.
x^{2}+x-48-3x=0
Tangohia te 3x mai i ngā taha e rua.
x^{2}-2x-48=0
Pahekotia te x me -3x, ka -2x.
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 tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. 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=-8 b=6
Ko te otinga te takirua ka hoatu i te tapeke -2.
\left(x^{2}-8x\right)+\left(6x-48\right)
Tuhia anō te x^{2}-2x-48 hei \left(x^{2}-8x\right)+\left(6x-48\right).
x\left(x-8\right)+6\left(x-8\right)
Tauwehea te x i te tuatahi me te 6 i te rōpū tuarua.
\left(x-8\right)\left(x+6\right)
Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.
x=8 x=-6
Hei kimi otinga whārite, me whakaoti te x-8=0 me te x+6=0.
x^{2}+x-48-3x=0
Tangohia te 3x mai i ngā taha e rua.
x^{2}-2x-48=0
Pahekotia te x me -3x, ka -2x.
x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-48\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±\sqrt{4-4\left(-48\right)}}{2}
Pūrua -2.
x=\frac{-\left(-2\right)±\sqrt{4+192}}{2}
Whakareatia -4 ki te -48.
x=\frac{-\left(-2\right)±\sqrt{196}}{2}
Tāpiri 4 ki te 192.
x=\frac{-\left(-2\right)±14}{2}
Tuhia te pūtakerua o te 196.
x=\frac{2±14}{2}
Ko te tauaro o -2 ko 2.
x=\frac{16}{2}
Nā, me whakaoti te whārite x=\frac{2±14}{2} ina he tāpiri te ±. Tāpiri 2 ki te 14.
x=8
Whakawehe 16 ki te 2.
x=-\frac{12}{2}
Nā, me whakaoti te whārite x=\frac{2±14}{2} ina he tango te ±. Tango 14 mai i 2.
x=-6
Whakawehe -12 ki te 2.
x=8 x=-6
Kua oti te whārite te whakatau.
x^{2}+x-48-3x=0
Tangohia te 3x mai i ngā taha e rua.
x^{2}-2x-48=0
Pahekotia te x me -3x, ka -2x.
x^{2}-2x=48
Me tāpiri te 48 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.
x^{2}-2x+1=48+1
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=49
Tāpiri 48 ki te 1.
\left(x-1\right)^{2}=49
Tauwehea te x^{2}-2x+1. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe 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=8 x=-6
Me tāpiri 1 ki ngā taha e rua o te whārite.