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x^{2}+28x+196-\left(x+11\right)^{2}=\left(x-6\right)^{2}
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+14\right)^{2}.
x^{2}+28x+196-\left(x^{2}+22x+121\right)=\left(x-6\right)^{2}
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+11\right)^{2}.
x^{2}+28x+196-x^{2}-22x-121=\left(x-6\right)^{2}
Hei kimi i te tauaro o x^{2}+22x+121, kimihia te tauaro o ia taurangi.
28x+196-22x-121=\left(x-6\right)^{2}
Pahekotia te x^{2} me -x^{2}, ka 0.
6x+196-121=\left(x-6\right)^{2}
Pahekotia te 28x me -22x, ka 6x.
6x+75=\left(x-6\right)^{2}
Tangohia te 121 i te 196, ka 75.
6x+75=x^{2}-12x+36
Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-6\right)^{2}.
6x+75-x^{2}=-12x+36
Tangohia te x^{2} mai i ngā taha e rua.
6x+75-x^{2}+12x=36
Me tāpiri te 12x ki ngā taha e rua.
18x+75-x^{2}=36
Pahekotia te 6x me 12x, ka 18x.
18x+75-x^{2}-36=0
Tangohia te 36 mai i ngā taha e rua.
18x+39-x^{2}=0
Tangohia te 36 i te 75, ka 39.
-x^{2}+18x+39=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{-18±\sqrt{18^{2}-4\left(-1\right)\times 39}}{2\left(-1\right)}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 18 mō b, me 39 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-18±\sqrt{324-4\left(-1\right)\times 39}}{2\left(-1\right)}
Pūrua 18.
x=\frac{-18±\sqrt{324+4\times 39}}{2\left(-1\right)}
Whakareatia -4 ki te -1.
x=\frac{-18±\sqrt{324+156}}{2\left(-1\right)}
Whakareatia 4 ki te 39.
x=\frac{-18±\sqrt{480}}{2\left(-1\right)}
Tāpiri 324 ki te 156.
x=\frac{-18±4\sqrt{30}}{2\left(-1\right)}
Tuhia te pūtakerua o te 480.
x=\frac{-18±4\sqrt{30}}{-2}
Whakareatia 2 ki te -1.
x=\frac{4\sqrt{30}-18}{-2}
Nā, me whakaoti te whārite x=\frac{-18±4\sqrt{30}}{-2} ina he tāpiri te ±. Tāpiri -18 ki te 4\sqrt{30}.
x=9-2\sqrt{30}
Whakawehe -18+4\sqrt{30} ki te -2.
x=\frac{-4\sqrt{30}-18}{-2}
Nā, me whakaoti te whārite x=\frac{-18±4\sqrt{30}}{-2} ina he tango te ±. Tango 4\sqrt{30} mai i -18.
x=2\sqrt{30}+9
Whakawehe -18-4\sqrt{30} ki te -2.
x=9-2\sqrt{30} x=2\sqrt{30}+9
Kua oti te whārite te whakatau.
x^{2}+28x+196-\left(x+11\right)^{2}=\left(x-6\right)^{2}
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+14\right)^{2}.
x^{2}+28x+196-\left(x^{2}+22x+121\right)=\left(x-6\right)^{2}
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+11\right)^{2}.
x^{2}+28x+196-x^{2}-22x-121=\left(x-6\right)^{2}
Hei kimi i te tauaro o x^{2}+22x+121, kimihia te tauaro o ia taurangi.
28x+196-22x-121=\left(x-6\right)^{2}
Pahekotia te x^{2} me -x^{2}, ka 0.
6x+196-121=\left(x-6\right)^{2}
Pahekotia te 28x me -22x, ka 6x.
6x+75=\left(x-6\right)^{2}
Tangohia te 121 i te 196, ka 75.
6x+75=x^{2}-12x+36
Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-6\right)^{2}.
6x+75-x^{2}=-12x+36
Tangohia te x^{2} mai i ngā taha e rua.
6x+75-x^{2}+12x=36
Me tāpiri te 12x ki ngā taha e rua.
18x+75-x^{2}=36
Pahekotia te 6x me 12x, ka 18x.
18x-x^{2}=36-75
Tangohia te 75 mai i ngā taha e rua.
18x-x^{2}=-39
Tangohia te 75 i te 36, ka -39.
-x^{2}+18x=-39
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{-x^{2}+18x}{-1}=-\frac{39}{-1}
Whakawehea ngā taha e rua ki te -1.
x^{2}+\frac{18}{-1}x=-\frac{39}{-1}
Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.
x^{2}-18x=-\frac{39}{-1}
Whakawehe 18 ki te -1.
x^{2}-18x=39
Whakawehe -39 ki te -1.
x^{2}-18x+\left(-9\right)^{2}=39+\left(-9\right)^{2}
Whakawehea te -18, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -9. Nā, tāpiria te pūrua o te -9 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-18x+81=39+81
Pūrua -9.
x^{2}-18x+81=120
Tāpiri 39 ki te 81.
\left(x-9\right)^{2}=120
Tauwehea x^{2}-18x+81. 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-9\right)^{2}}=\sqrt{120}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-9=2\sqrt{30} x-9=-2\sqrt{30}
Whakarūnātia.
x=2\sqrt{30}+9 x=9-2\sqrt{30}
Me tāpiri 9 ki ngā taha e rua o te whārite.