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a+b=6 ab=1\left(-40\right)=-40
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-40. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,40 -2,20 -4,10 -5,8
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 -40.
-1+40=39 -2+20=18 -4+10=6 -5+8=3
Tātaihia te tapeke mō ia takirua.
a=-4 b=10
Ko te otinga te takirua ka hoatu i te tapeke 6.
\left(x^{2}-4x\right)+\left(10x-40\right)
Tuhia anō te x^{2}+6x-40 hei \left(x^{2}-4x\right)+\left(10x-40\right).
x\left(x-4\right)+10\left(x-4\right)
Tauwehea te x i te tuatahi me te 10 i te rōpū tuarua.
\left(x-4\right)\left(x+10\right)
Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}+6x-40=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{-6±\sqrt{6^{2}-4\left(-40\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{-6±\sqrt{36-4\left(-40\right)}}{2}
Pūrua 6.
x=\frac{-6±\sqrt{36+160}}{2}
Whakareatia -4 ki te -40.
x=\frac{-6±\sqrt{196}}{2}
Tāpiri 36 ki te 160.
x=\frac{-6±14}{2}
Tuhia te pūtakerua o te 196.
x=\frac{8}{2}
Nā, me whakaoti te whārite x=\frac{-6±14}{2} ina he tāpiri te ±. Tāpiri -6 ki te 14.
x=4
Whakawehe 8 ki te 2.
x=-\frac{20}{2}
Nā, me whakaoti te whārite x=\frac{-6±14}{2} ina he tango te ±. Tango 14 mai i -6.
x=-10
Whakawehe -20 ki te 2.
x^{2}+6x-40=\left(x-4\right)\left(x-\left(-10\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 4 mō te x_{1} me te -10 mō te x_{2}.
x^{2}+6x-40=\left(x-4\right)\left(x+10\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.