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a+b=-4 ab=1\left(-12\right)=-12
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-12 2,-6 3,-4
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 -12.
1-12=-11 2-6=-4 3-4=-1
Tātaihia te tapeke mō ia takirua.
a=-6 b=2
Ko te otinga te takirua ka hoatu i te tapeke -4.
\left(x^{2}-6x\right)+\left(2x-12\right)
Tuhia anō te x^{2}-4x-12 hei \left(x^{2}-6x\right)+\left(2x-12\right).
x\left(x-6\right)+2\left(x-6\right)
Tauwehea te x i te tuatahi me te 2 i te rōpū tuarua.
\left(x-6\right)\left(x+2\right)
Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}-4x-12=0
Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.
x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-12\right)}}{2}
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{-\left(-4\right)±\sqrt{16-4\left(-12\right)}}{2}
Pūrua -4.
x=\frac{-\left(-4\right)±\sqrt{16+48}}{2}
Whakareatia -4 ki te -12.
x=\frac{-\left(-4\right)±\sqrt{64}}{2}
Tāpiri 16 ki te 48.
x=\frac{-\left(-4\right)±8}{2}
Tuhia te pūtakerua o te 64.
x=\frac{4±8}{2}
Ko te tauaro o -4 ko 4.
x=\frac{12}{2}
Nā, me whakaoti te whārite x=\frac{4±8}{2} ina he tāpiri te ±. Tāpiri 4 ki te 8.
x=6
Whakawehe 12 ki te 2.
x=-\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{4±8}{2} ina he tango te ±. Tango 8 mai i 4.
x=-2
Whakawehe -4 ki te 2.
x^{2}-4x-12=\left(x-6\right)\left(x-\left(-2\right)\right)
Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 6 mō te x_{1} me te -2 mō te x_{2}.
x^{2}-4x-12=\left(x-6\right)\left(x+2\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.