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\left(x-2\right)\times 2+\left(x-3\right)\times 3=3\left(x-3\right)\left(x-2\right)
Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 2,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-3\right)\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-3,x-2.
2x-4+\left(x-3\right)\times 3=3\left(x-3\right)\left(x-2\right)
Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 2.
2x-4+3x-9=3\left(x-3\right)\left(x-2\right)
Whakamahia te āhuatanga tohatoha hei whakarea te x-3 ki te 3.
5x-4-9=3\left(x-3\right)\left(x-2\right)
Pahekotia te 2x me 3x, ka 5x.
5x-13=3\left(x-3\right)\left(x-2\right)
Tangohia te 9 i te -4, ka -13.
5x-13=\left(3x-9\right)\left(x-2\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-3.
5x-13=3x^{2}-15x+18
Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-9 ki te x-2 ka whakakotahi i ngā kupu rite.
5x-13-3x^{2}=-15x+18
Tangohia te 3x^{2} mai i ngā taha e rua.
5x-13-3x^{2}+15x=18
Me tāpiri te 15x ki ngā taha e rua.
20x-13-3x^{2}=18
Pahekotia te 5x me 15x, ka 20x.
20x-13-3x^{2}-18=0
Tangohia te 18 mai i ngā taha e rua.
20x-31-3x^{2}=0
Tangohia te 18 i te -13, ka -31.
-3x^{2}+20x-31=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{-20±\sqrt{20^{2}-4\left(-3\right)\left(-31\right)}}{2\left(-3\right)}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 20 mō b, me -31 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-20±\sqrt{400-4\left(-3\right)\left(-31\right)}}{2\left(-3\right)}
Pūrua 20.
x=\frac{-20±\sqrt{400+12\left(-31\right)}}{2\left(-3\right)}
Whakareatia -4 ki te -3.
x=\frac{-20±\sqrt{400-372}}{2\left(-3\right)}
Whakareatia 12 ki te -31.
x=\frac{-20±\sqrt{28}}{2\left(-3\right)}
Tāpiri 400 ki te -372.
x=\frac{-20±2\sqrt{7}}{2\left(-3\right)}
Tuhia te pūtakerua o te 28.
x=\frac{-20±2\sqrt{7}}{-6}
Whakareatia 2 ki te -3.
x=\frac{2\sqrt{7}-20}{-6}
Nā, me whakaoti te whārite x=\frac{-20±2\sqrt{7}}{-6} ina he tāpiri te ±. Tāpiri -20 ki te 2\sqrt{7}.
x=\frac{10-\sqrt{7}}{3}
Whakawehe -20+2\sqrt{7} ki te -6.
x=\frac{-2\sqrt{7}-20}{-6}
Nā, me whakaoti te whārite x=\frac{-20±2\sqrt{7}}{-6} ina he tango te ±. Tango 2\sqrt{7} mai i -20.
x=\frac{\sqrt{7}+10}{3}
Whakawehe -20-2\sqrt{7} ki te -6.
x=\frac{10-\sqrt{7}}{3} x=\frac{\sqrt{7}+10}{3}
Kua oti te whārite te whakatau.
\left(x-2\right)\times 2+\left(x-3\right)\times 3=3\left(x-3\right)\left(x-2\right)
Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 2,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-3\right)\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-3,x-2.
2x-4+\left(x-3\right)\times 3=3\left(x-3\right)\left(x-2\right)
Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 2.
2x-4+3x-9=3\left(x-3\right)\left(x-2\right)
Whakamahia te āhuatanga tohatoha hei whakarea te x-3 ki te 3.
5x-4-9=3\left(x-3\right)\left(x-2\right)
Pahekotia te 2x me 3x, ka 5x.
5x-13=3\left(x-3\right)\left(x-2\right)
Tangohia te 9 i te -4, ka -13.
5x-13=\left(3x-9\right)\left(x-2\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-3.
5x-13=3x^{2}-15x+18
Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-9 ki te x-2 ka whakakotahi i ngā kupu rite.
5x-13-3x^{2}=-15x+18
Tangohia te 3x^{2} mai i ngā taha e rua.
5x-13-3x^{2}+15x=18
Me tāpiri te 15x ki ngā taha e rua.
20x-13-3x^{2}=18
Pahekotia te 5x me 15x, ka 20x.
20x-3x^{2}=18+13
Me tāpiri te 13 ki ngā taha e rua.
20x-3x^{2}=31
Tāpirihia te 18 ki te 13, ka 31.
-3x^{2}+20x=31
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.
\frac{-3x^{2}+20x}{-3}=\frac{31}{-3}
Whakawehea ngā taha e rua ki te -3.
x^{2}+\frac{20}{-3}x=\frac{31}{-3}
Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.
x^{2}-\frac{20}{3}x=\frac{31}{-3}
Whakawehe 20 ki te -3.
x^{2}-\frac{20}{3}x=-\frac{31}{3}
Whakawehe 31 ki te -3.
x^{2}-\frac{20}{3}x+\left(-\frac{10}{3}\right)^{2}=-\frac{31}{3}+\left(-\frac{10}{3}\right)^{2}
Whakawehea te -\frac{20}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{10}{3}. Nā, tāpiria te pūrua o te -\frac{10}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-\frac{20}{3}x+\frac{100}{9}=-\frac{31}{3}+\frac{100}{9}
Pūruatia -\frac{10}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-\frac{20}{3}x+\frac{100}{9}=\frac{7}{9}
Tāpiri -\frac{31}{3} ki te \frac{100}{9} 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.
\left(x-\frac{10}{3}\right)^{2}=\frac{7}{9}
Tauwehea x^{2}-\frac{20}{3}x+\frac{100}{9}. 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{10}{3}\right)^{2}}=\sqrt{\frac{7}{9}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{10}{3}=\frac{\sqrt{7}}{3} x-\frac{10}{3}=-\frac{\sqrt{7}}{3}
Whakarūnātia.
x=\frac{\sqrt{7}+10}{3} x=\frac{10-\sqrt{7}}{3}
Me tāpiri \frac{10}{3} ki ngā taha e rua o te whārite.