Whakaoti mō x
x=\frac{1}{2}=0.5
x=4
Graph
Tohaina
Kua tāruatia ki te papatopenga
a+b=-9 ab=2\times 4=8
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 2x^{2}+ax+bx+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,-8 -2,-4
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 8.
-1-8=-9 -2-4=-6
Tātaihia te tapeke mō ia takirua.
a=-8 b=-1
Ko te otinga te takirua ka hoatu i te tapeke -9.
\left(2x^{2}-8x\right)+\left(-x+4\right)
Tuhia anō te 2x^{2}-9x+4 hei \left(2x^{2}-8x\right)+\left(-x+4\right).
2x\left(x-4\right)-\left(x-4\right)
Tauwehea te 2x i te tuatahi me te -1 i te rōpū tuarua.
\left(x-4\right)\left(2x-1\right)
Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.
x=4 x=\frac{1}{2}
Hei kimi otinga whārite, me whakaoti te x-4=0 me te 2x-1=0.
2x^{2}-9x+4=0
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(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 2\times 4}}{2\times 2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -9 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-9\right)±\sqrt{81-4\times 2\times 4}}{2\times 2}
Pūrua -9.
x=\frac{-\left(-9\right)±\sqrt{81-8\times 4}}{2\times 2}
Whakareatia -4 ki te 2.
x=\frac{-\left(-9\right)±\sqrt{81-32}}{2\times 2}
Whakareatia -8 ki te 4.
x=\frac{-\left(-9\right)±\sqrt{49}}{2\times 2}
Tāpiri 81 ki te -32.
x=\frac{-\left(-9\right)±7}{2\times 2}
Tuhia te pūtakerua o te 49.
x=\frac{9±7}{2\times 2}
Ko te tauaro o -9 ko 9.
x=\frac{9±7}{4}
Whakareatia 2 ki te 2.
x=\frac{16}{4}
Nā, me whakaoti te whārite x=\frac{9±7}{4} ina he tāpiri te ±. Tāpiri 9 ki te 7.
x=4
Whakawehe 16 ki te 4.
x=\frac{2}{4}
Nā, me whakaoti te whārite x=\frac{9±7}{4} ina he tango te ±. Tango 7 mai i 9.
x=\frac{1}{2}
Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
x=4 x=\frac{1}{2}
Kua oti te whārite te whakatau.
2x^{2}-9x+4=0
Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.
2x^{2}-9x+4-4=-4
Me tango 4 mai i ngā taha e rua o te whārite.
2x^{2}-9x=-4
Mā te tango i te 4 i a ia ake anō ka toe ko te 0.
\frac{2x^{2}-9x}{2}=-\frac{4}{2}
Whakawehea ngā taha e rua ki te 2.
x^{2}-\frac{9}{2}x=-\frac{4}{2}
Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.
x^{2}-\frac{9}{2}x=-2
Whakawehe -4 ki te 2.
x^{2}-\frac{9}{2}x+\left(-\frac{9}{4}\right)^{2}=-2+\left(-\frac{9}{4}\right)^{2}
Whakawehea te -\frac{9}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{4}. Nā, tāpiria te pūrua o te -\frac{9}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-\frac{9}{2}x+\frac{81}{16}=-2+\frac{81}{16}
Pūruatia -\frac{9}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-\frac{9}{2}x+\frac{81}{16}=\frac{49}{16}
Tāpiri -2 ki te \frac{81}{16}.
\left(x-\frac{9}{4}\right)^{2}=\frac{49}{16}
Tauwehea x^{2}-\frac{9}{2}x+\frac{81}{16}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-\frac{9}{4}\right)^{2}}=\sqrt{\frac{49}{16}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{9}{4}=\frac{7}{4} x-\frac{9}{4}=-\frac{7}{4}
Whakarūnātia.
x=4 x=\frac{1}{2}
Me tāpiri \frac{9}{4} ki ngā taha e rua o te whārite.
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