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a+b=8 ab=1\times 7=7
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+7. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=1 b=7
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(7x+7\right)
Tuhia anō te x^{2}+8x+7 hei \left(x^{2}+x\right)+\left(7x+7\right).
x\left(x+1\right)+7\left(x+1\right)
Tauwehea te x i te tuatahi me te 7 i te rōpū tuarua.
\left(x+1\right)\left(x+7\right)
Whakatauwehea atu te kīanga pātahi x+1 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}+8x+7=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{-8±\sqrt{8^{2}-4\times 7}}{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{-8±\sqrt{64-4\times 7}}{2}
Pūrua 8.
x=\frac{-8±\sqrt{64-28}}{2}
Whakareatia -4 ki te 7.
x=\frac{-8±\sqrt{36}}{2}
Tāpiri 64 ki te -28.
x=\frac{-8±6}{2}
Tuhia te pūtakerua o te 36.
x=-\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{-8±6}{2} ina he tāpiri te ±. Tāpiri -8 ki te 6.
x=-1
Whakawehe -2 ki te 2.
x=-\frac{14}{2}
Nā, me whakaoti te whārite x=\frac{-8±6}{2} ina he tango te ±. Tango 6 mai i -8.
x=-7
Whakawehe -14 ki te 2.
x^{2}+8x+7=\left(x-\left(-1\right)\right)\left(x-\left(-7\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 -1 mō te x_{1} me te -7 mō te x_{2}.
x^{2}+8x+7=\left(x+1\right)\left(x+7\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.