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a+b=-9 ab=5\left(-18\right)=-90
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 5y^{2}+ay+by-18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-90 2,-45 3,-30 5,-18 6,-15 9,-10
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 -90.
1-90=-89 2-45=-43 3-30=-27 5-18=-13 6-15=-9 9-10=-1
Tātaihia te tapeke mō ia takirua.
a=-15 b=6
Ko te otinga te takirua ka hoatu i te tapeke -9.
\left(5y^{2}-15y\right)+\left(6y-18\right)
Tuhia anō te 5y^{2}-9y-18 hei \left(5y^{2}-15y\right)+\left(6y-18\right).
5y\left(y-3\right)+6\left(y-3\right)
Tauwehea te 5y i te tuatahi me te 6 i te rōpū tuarua.
\left(y-3\right)\left(5y+6\right)
Whakatauwehea atu te kīanga pātahi y-3 mā te whakamahi i te āhuatanga tātai tohatoha.
5y^{2}-9y-18=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.
y=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 5\left(-18\right)}}{2\times 5}
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.
y=\frac{-\left(-9\right)±\sqrt{81-4\times 5\left(-18\right)}}{2\times 5}
Pūrua -9.
y=\frac{-\left(-9\right)±\sqrt{81-20\left(-18\right)}}{2\times 5}
Whakareatia -4 ki te 5.
y=\frac{-\left(-9\right)±\sqrt{81+360}}{2\times 5}
Whakareatia -20 ki te -18.
y=\frac{-\left(-9\right)±\sqrt{441}}{2\times 5}
Tāpiri 81 ki te 360.
y=\frac{-\left(-9\right)±21}{2\times 5}
Tuhia te pūtakerua o te 441.
y=\frac{9±21}{2\times 5}
Ko te tauaro o -9 ko 9.
y=\frac{9±21}{10}
Whakareatia 2 ki te 5.
y=\frac{30}{10}
Nā, me whakaoti te whārite y=\frac{9±21}{10} ina he tāpiri te ±. Tāpiri 9 ki te 21.
y=3
Whakawehe 30 ki te 10.
y=-\frac{12}{10}
Nā, me whakaoti te whārite y=\frac{9±21}{10} ina he tango te ±. Tango 21 mai i 9.
y=-\frac{6}{5}
Whakahekea te hautanga \frac{-12}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
5y^{2}-9y-18=5\left(y-3\right)\left(y-\left(-\frac{6}{5}\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 3 mō te x_{1} me te -\frac{6}{5} mō te x_{2}.
5y^{2}-9y-18=5\left(y-3\right)\left(y+\frac{6}{5}\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.
5y^{2}-9y-18=5\left(y-3\right)\times \frac{5y+6}{5}
Tāpiri \frac{6}{5} ki te y mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
5y^{2}-9y-18=\left(y-3\right)\left(5y+6\right)
Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 5 me te 5.