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400\left(x-284\right)^{2}=x^{2}
Tē taea kia ōrite te tāupe x ki 284 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-284\right)^{2}.
400\left(x^{2}-568x+80656\right)=x^{2}
Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-284\right)^{2}.
400x^{2}-227200x+32262400=x^{2}
Whakamahia te āhuatanga tohatoha hei whakarea te 400 ki te x^{2}-568x+80656.
400x^{2}-227200x+32262400-x^{2}=0
Tangohia te x^{2} mai i ngā taha e rua.
399x^{2}-227200x+32262400=0
Pahekotia te 400x^{2} me -x^{2}, ka 399x^{2}.
x=\frac{-\left(-227200\right)±\sqrt{\left(-227200\right)^{2}-4\times 399\times 32262400}}{2\times 399}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 399 mō a, -227200 mō b, me 32262400 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-227200\right)±\sqrt{51619840000-4\times 399\times 32262400}}{2\times 399}
Pūrua -227200.
x=\frac{-\left(-227200\right)±\sqrt{51619840000-1596\times 32262400}}{2\times 399}
Whakareatia -4 ki te 399.
x=\frac{-\left(-227200\right)±\sqrt{51619840000-51490790400}}{2\times 399}
Whakareatia -1596 ki te 32262400.
x=\frac{-\left(-227200\right)±\sqrt{129049600}}{2\times 399}
Tāpiri 51619840000 ki te -51490790400.
x=\frac{-\left(-227200\right)±11360}{2\times 399}
Tuhia te pūtakerua o te 129049600.
x=\frac{227200±11360}{2\times 399}
Ko te tauaro o -227200 ko 227200.
x=\frac{227200±11360}{798}
Whakareatia 2 ki te 399.
x=\frac{238560}{798}
Nā, me whakaoti te whārite x=\frac{227200±11360}{798} ina he tāpiri te ±. Tāpiri 227200 ki te 11360.
x=\frac{5680}{19}
Whakahekea te hautanga \frac{238560}{798} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 42.
x=\frac{215840}{798}
Nā, me whakaoti te whārite x=\frac{227200±11360}{798} ina he tango te ±. Tango 11360 mai i 227200.
x=\frac{5680}{21}
Whakahekea te hautanga \frac{215840}{798} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 38.
x=\frac{5680}{19} x=\frac{5680}{21}
Kua oti te whārite te whakatau.
400\left(x-284\right)^{2}=x^{2}
Tē taea kia ōrite te tāupe x ki 284 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-284\right)^{2}.
400\left(x^{2}-568x+80656\right)=x^{2}
Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-284\right)^{2}.
400x^{2}-227200x+32262400=x^{2}
Whakamahia te āhuatanga tohatoha hei whakarea te 400 ki te x^{2}-568x+80656.
400x^{2}-227200x+32262400-x^{2}=0
Tangohia te x^{2} mai i ngā taha e rua.
399x^{2}-227200x+32262400=0
Pahekotia te 400x^{2} me -x^{2}, ka 399x^{2}.
399x^{2}-227200x=-32262400
Tangohia te 32262400 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
\frac{399x^{2}-227200x}{399}=-\frac{32262400}{399}
Whakawehea ngā taha e rua ki te 399.
x^{2}-\frac{227200}{399}x=-\frac{32262400}{399}
Mā te whakawehe ki te 399 ka wetekia te whakareanga ki te 399.
x^{2}-\frac{227200}{399}x+\left(-\frac{113600}{399}\right)^{2}=-\frac{32262400}{399}+\left(-\frac{113600}{399}\right)^{2}
Whakawehea te -\frac{227200}{399}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{113600}{399}. Nā, tāpiria te pūrua o te -\frac{113600}{399} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-\frac{227200}{399}x+\frac{12904960000}{159201}=-\frac{32262400}{399}+\frac{12904960000}{159201}
Pūruatia -\frac{113600}{399} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-\frac{227200}{399}x+\frac{12904960000}{159201}=\frac{32262400}{159201}
Tāpiri -\frac{32262400}{399} ki te \frac{12904960000}{159201} 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{113600}{399}\right)^{2}=\frac{32262400}{159201}
Tauwehea x^{2}-\frac{227200}{399}x+\frac{12904960000}{159201}. 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{113600}{399}\right)^{2}}=\sqrt{\frac{32262400}{159201}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{113600}{399}=\frac{5680}{399} x-\frac{113600}{399}=-\frac{5680}{399}
Whakarūnātia.
x=\frac{5680}{19} x=\frac{5680}{21}
Me tāpiri \frac{113600}{399} ki ngā taha e rua o te whārite.