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x^{2}+10x+25=0
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+5\right)^{2}.
a+b=10 ab=25
Hei whakaoti i te whārite, whakatauwehea te x^{2}+10x+25 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,25 5,5
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 25.
1+25=26 5+5=10
Tātaihia te tapeke mō ia takirua.
a=5 b=5
Ko te otinga te takirua ka hoatu i te tapeke 10.
\left(x+5\right)\left(x+5\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
\left(x+5\right)^{2}
Tuhia anōtia hei pūrua huarua.
x=-5
Hei kimi i te otinga whārite, whakaotia te x+5=0.
x^{2}+10x+25=0
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+5\right)^{2}.
a+b=10 ab=1\times 25=25
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+25. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,25 5,5
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 25.
1+25=26 5+5=10
Tātaihia te tapeke mō ia takirua.
a=5 b=5
Ko te otinga te takirua ka hoatu i te tapeke 10.
\left(x^{2}+5x\right)+\left(5x+25\right)
Tuhia anō te x^{2}+10x+25 hei \left(x^{2}+5x\right)+\left(5x+25\right).
x\left(x+5\right)+5\left(x+5\right)
Tauwehea te x i te tuatahi me te 5 i te rōpū tuarua.
\left(x+5\right)\left(x+5\right)
Whakatauwehea atu te kīanga pātahi x+5 mā te whakamahi i te āhuatanga tātai tohatoha.
\left(x+5\right)^{2}
Tuhia anōtia hei pūrua huarua.
x=-5
Hei kimi i te otinga whārite, whakaotia te x+5=0.
x^{2}+10x+25=0
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+5\right)^{2}.
x=\frac{-10±\sqrt{10^{2}-4\times 25}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 10 mō b, me 25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-10±\sqrt{100-4\times 25}}{2}
Pūrua 10.
x=\frac{-10±\sqrt{100-100}}{2}
Whakareatia -4 ki te 25.
x=\frac{-10±\sqrt{0}}{2}
Tāpiri 100 ki te -100.
x=-\frac{10}{2}
Tuhia te pūtakerua o te 0.
x=-5
Whakawehe -10 ki te 2.
\sqrt{\left(x+5\right)^{2}}=\sqrt{0}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+5=0 x+5=0
Whakarūnātia.
x=-5 x=-5
Me tango 5 mai i ngā taha e rua o te whārite.
x=-5
Kua oti te whārite te whakatau. He ōrite ngā whakatau.