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a+b=-16 ab=1\times 28=28
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+28. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,-28 -2,-14 -4,-7
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 28.
-1-28=-29 -2-14=-16 -4-7=-11
Tātaihia te tapeke mō ia takirua.
a=-14 b=-2
Ko te otinga te takirua ka hoatu i te tapeke -16.
\left(x^{2}-14x\right)+\left(-2x+28\right)
Tuhia anō te x^{2}-16x+28 hei \left(x^{2}-14x\right)+\left(-2x+28\right).
x\left(x-14\right)-2\left(x-14\right)
Tauwehea te x i te tuatahi me te -2 i te rōpū tuarua.
\left(x-14\right)\left(x-2\right)
Whakatauwehea atu te kīanga pātahi x-14 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}-16x+28=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(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 28}}{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(-16\right)±\sqrt{256-4\times 28}}{2}
Pūrua -16.
x=\frac{-\left(-16\right)±\sqrt{256-112}}{2}
Whakareatia -4 ki te 28.
x=\frac{-\left(-16\right)±\sqrt{144}}{2}
Tāpiri 256 ki te -112.
x=\frac{-\left(-16\right)±12}{2}
Tuhia te pūtakerua o te 144.
x=\frac{16±12}{2}
Ko te tauaro o -16 ko 16.
x=\frac{28}{2}
Nā, me whakaoti te whārite x=\frac{16±12}{2} ina he tāpiri te ±. Tāpiri 16 ki te 12.
x=14
Whakawehe 28 ki te 2.
x=\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{16±12}{2} ina he tango te ±. Tango 12 mai i 16.
x=2
Whakawehe 4 ki te 2.
x^{2}-16x+28=\left(x-14\right)\left(x-2\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 14 mō te x_{1} me te 2 mō te x_{2}.