Whakaoti mō x
x=-5
x=-1
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{2}+4+8x-2x=-1
Tangohia te 2x mai i ngā taha e rua.
x^{2}+4+6x=-1
Pahekotia te 8x me -2x, ka 6x.
x^{2}+4+6x+1=0
Me tāpiri te 1 ki ngā taha e rua.
x^{2}+5+6x=0
Tāpirihia te 4 ki te 1, ka 5.
x^{2}+6x+5=0
Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.
a+b=6 ab=5
Hei whakaoti i te whārite, whakatauwehea te x^{2}+6x+5 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.
a=1 b=5
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. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x+1\right)\left(x+5\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=-1 x=-5
Hei kimi otinga whārite, me whakaoti te x+1=0 me te x+5=0.
x^{2}+4+8x-2x=-1
Tangohia te 2x mai i ngā taha e rua.
x^{2}+4+6x=-1
Pahekotia te 8x me -2x, ka 6x.
x^{2}+4+6x+1=0
Me tāpiri te 1 ki ngā taha e rua.
x^{2}+5+6x=0
Tāpirihia te 4 ki te 1, ka 5.
x^{2}+6x+5=0
Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.
a+b=6 ab=1\times 5=5
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=1 b=5
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. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x^{2}+x\right)+\left(5x+5\right)
Tuhia anō te x^{2}+6x+5 hei \left(x^{2}+x\right)+\left(5x+5\right).
x\left(x+1\right)+5\left(x+1\right)
Tauwehea te x i te tuatahi me te 5 i te rōpū tuarua.
\left(x+1\right)\left(x+5\right)
Whakatauwehea atu te kīanga pātahi x+1 mā te whakamahi i te āhuatanga tātai tohatoha.
x=-1 x=-5
Hei kimi otinga whārite, me whakaoti te x+1=0 me te x+5=0.
x^{2}+4+8x-2x=-1
Tangohia te 2x mai i ngā taha e rua.
x^{2}+4+6x=-1
Pahekotia te 8x me -2x, ka 6x.
x^{2}+4+6x+1=0
Me tāpiri te 1 ki ngā taha e rua.
x^{2}+5+6x=0
Tāpirihia te 4 ki te 1, ka 5.
x^{2}+6x+5=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{-6±\sqrt{6^{2}-4\times 5}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-6±\sqrt{36-4\times 5}}{2}
Pūrua 6.
x=\frac{-6±\sqrt{36-20}}{2}
Whakareatia -4 ki te 5.
x=\frac{-6±\sqrt{16}}{2}
Tāpiri 36 ki te -20.
x=\frac{-6±4}{2}
Tuhia te pūtakerua o te 16.
x=-\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{-6±4}{2} ina he tāpiri te ±. Tāpiri -6 ki te 4.
x=-1
Whakawehe -2 ki te 2.
x=-\frac{10}{2}
Nā, me whakaoti te whārite x=\frac{-6±4}{2} ina he tango te ±. Tango 4 mai i -6.
x=-5
Whakawehe -10 ki te 2.
x=-1 x=-5
Kua oti te whārite te whakatau.
x^{2}+4+8x-2x=-1
Tangohia te 2x mai i ngā taha e rua.
x^{2}+4+6x=-1
Pahekotia te 8x me -2x, ka 6x.
x^{2}+6x=-1-4
Tangohia te 4 mai i ngā taha e rua.
x^{2}+6x=-5
Tangohia te 4 i te -1, ka -5.
x^{2}+6x+3^{2}=-5+3^{2}
Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+6x+9=-5+9
Pūrua 3.
x^{2}+6x+9=4
Tāpiri -5 ki te 9.
\left(x+3\right)^{2}=4
Tauwehea x^{2}+6x+9. 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+3\right)^{2}}=\sqrt{4}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+3=2 x+3=-2
Whakarūnātia.
x=-1 x=-5
Me tango 3 mai i ngā taha e rua o te whārite.
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