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\left(x+72\right)\left(-36\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x
Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -72,36 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-36\right)\left(x+72\right), arā, te tauraro pātahi he tino iti rawa te kitea o -36+x,72+x.
\left(-36x-2592\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tohatoha hei whakarea te x+72 ki te -36.
-36x^{2}-2592x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tohatoha hei whakarea te -36x-2592 ki te x.
-36x^{2}-2592x=\left(x^{2}+36x-2592\right)\times 36+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tuaritanga hei whakarea te x-36 ki te x+72 ka whakakotahi i ngā kupu rite.
-36x^{2}-2592x=36x^{2}+1296x-93312+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+36x-2592 ki te 36.
-36x^{2}-2592x=36x^{2}+1296x-93312+\left(72x-2592\right)x
Whakamahia te āhuatanga tohatoha hei whakarea te x-36 ki te 72.
-36x^{2}-2592x=36x^{2}+1296x-93312+72x^{2}-2592x
Whakamahia te āhuatanga tohatoha hei whakarea te 72x-2592 ki te x.
-36x^{2}-2592x=108x^{2}+1296x-93312-2592x
Pahekotia te 36x^{2} me 72x^{2}, ka 108x^{2}.
-36x^{2}-2592x=108x^{2}-1296x-93312
Pahekotia te 1296x me -2592x, ka -1296x.
-36x^{2}-2592x-108x^{2}=-1296x-93312
Tangohia te 108x^{2} mai i ngā taha e rua.
-144x^{2}-2592x=-1296x-93312
Pahekotia te -36x^{2} me -108x^{2}, ka -144x^{2}.
-144x^{2}-2592x+1296x=-93312
Me tāpiri te 1296x ki ngā taha e rua.
-144x^{2}-1296x=-93312
Pahekotia te -2592x me 1296x, ka -1296x.
-144x^{2}-1296x+93312=0
Me tāpiri te 93312 ki ngā taha e rua.
x=\frac{-\left(-1296\right)±\sqrt{\left(-1296\right)^{2}-4\left(-144\right)\times 93312}}{2\left(-144\right)}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -144 mō a, -1296 mō b, me 93312 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-1296\right)±\sqrt{1679616-4\left(-144\right)\times 93312}}{2\left(-144\right)}
Pūrua -1296.
x=\frac{-\left(-1296\right)±\sqrt{1679616+576\times 93312}}{2\left(-144\right)}
Whakareatia -4 ki te -144.
x=\frac{-\left(-1296\right)±\sqrt{1679616+53747712}}{2\left(-144\right)}
Whakareatia 576 ki te 93312.
x=\frac{-\left(-1296\right)±\sqrt{55427328}}{2\left(-144\right)}
Tāpiri 1679616 ki te 53747712.
x=\frac{-\left(-1296\right)±1296\sqrt{33}}{2\left(-144\right)}
Tuhia te pūtakerua o te 55427328.
x=\frac{1296±1296\sqrt{33}}{2\left(-144\right)}
Ko te tauaro o -1296 ko 1296.
x=\frac{1296±1296\sqrt{33}}{-288}
Whakareatia 2 ki te -144.
x=\frac{1296\sqrt{33}+1296}{-288}
Nā, me whakaoti te whārite x=\frac{1296±1296\sqrt{33}}{-288} ina he tāpiri te ±. Tāpiri 1296 ki te 1296\sqrt{33}.
x=\frac{-9\sqrt{33}-9}{2}
Whakawehe 1296+1296\sqrt{33} ki te -288.
x=\frac{1296-1296\sqrt{33}}{-288}
Nā, me whakaoti te whārite x=\frac{1296±1296\sqrt{33}}{-288} ina he tango te ±. Tango 1296\sqrt{33} mai i 1296.
x=\frac{9\sqrt{33}-9}{2}
Whakawehe 1296-1296\sqrt{33} ki te -288.
x=\frac{-9\sqrt{33}-9}{2} x=\frac{9\sqrt{33}-9}{2}
Kua oti te whārite te whakatau.
\left(x+72\right)\left(-36\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x
Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -72,36 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-36\right)\left(x+72\right), arā, te tauraro pātahi he tino iti rawa te kitea o -36+x,72+x.
\left(-36x-2592\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tohatoha hei whakarea te x+72 ki te -36.
-36x^{2}-2592x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tohatoha hei whakarea te -36x-2592 ki te x.
-36x^{2}-2592x=\left(x^{2}+36x-2592\right)\times 36+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tuaritanga hei whakarea te x-36 ki te x+72 ka whakakotahi i ngā kupu rite.
-36x^{2}-2592x=36x^{2}+1296x-93312+\left(x-36\right)\times 72x
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+36x-2592 ki te 36.
-36x^{2}-2592x=36x^{2}+1296x-93312+\left(72x-2592\right)x
Whakamahia te āhuatanga tohatoha hei whakarea te x-36 ki te 72.
-36x^{2}-2592x=36x^{2}+1296x-93312+72x^{2}-2592x
Whakamahia te āhuatanga tohatoha hei whakarea te 72x-2592 ki te x.
-36x^{2}-2592x=108x^{2}+1296x-93312-2592x
Pahekotia te 36x^{2} me 72x^{2}, ka 108x^{2}.
-36x^{2}-2592x=108x^{2}-1296x-93312
Pahekotia te 1296x me -2592x, ka -1296x.
-36x^{2}-2592x-108x^{2}=-1296x-93312
Tangohia te 108x^{2} mai i ngā taha e rua.
-144x^{2}-2592x=-1296x-93312
Pahekotia te -36x^{2} me -108x^{2}, ka -144x^{2}.
-144x^{2}-2592x+1296x=-93312
Me tāpiri te 1296x ki ngā taha e rua.
-144x^{2}-1296x=-93312
Pahekotia te -2592x me 1296x, ka -1296x.
\frac{-144x^{2}-1296x}{-144}=-\frac{93312}{-144}
Whakawehea ngā taha e rua ki te -144.
x^{2}+\left(-\frac{1296}{-144}\right)x=-\frac{93312}{-144}
Mā te whakawehe ki te -144 ka wetekia te whakareanga ki te -144.
x^{2}+9x=-\frac{93312}{-144}
Whakawehe -1296 ki te -144.
x^{2}+9x=648
Whakawehe -93312 ki te -144.
x^{2}+9x+\left(\frac{9}{2}\right)^{2}=648+\left(\frac{9}{2}\right)^{2}
Whakawehea te 9, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{9}{2}. Nā, tāpiria te pūrua o te \frac{9}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+9x+\frac{81}{4}=648+\frac{81}{4}
Pūruatia \frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+9x+\frac{81}{4}=\frac{2673}{4}
Tāpiri 648 ki te \frac{81}{4}.
\left(x+\frac{9}{2}\right)^{2}=\frac{2673}{4}
Tauwehea x^{2}+9x+\frac{81}{4}. 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}{2}\right)^{2}}=\sqrt{\frac{2673}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{9}{2}=\frac{9\sqrt{33}}{2} x+\frac{9}{2}=-\frac{9\sqrt{33}}{2}
Whakarūnātia.
x=\frac{9\sqrt{33}-9}{2} x=\frac{-9\sqrt{33}-9}{2}
Me tango \frac{9}{2} mai i ngā taha e rua o te whārite.