解:(1)移項得:3m
2-7m=4,
m
2-
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m=
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,
配方得:m
2-
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m+(
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)
2=
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+(
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)
2,
(m-
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)
2=
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,
開方得:m-
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=±
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,
m
1=
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,m
2=
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.
(2)
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,
(x+
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-1)
2=0,
開方得:x+
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-1=0,
x=1-
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,
即x
1=x
2=1-
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.
(3)(2x-5)
2-(x+4)
2=0,
[(2x-5)+(x+4)][(2x-5)-(x+4)]=0,
(3x-1)(x-9)=0,
3x-1=0,x-9=0,
x
1=
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,x
2=9.
(4)25(x+3)
2-16(x+2)
2=0,
25(x+3)
2=16(x+2)
2,
5(x+3)=±4(x+2),
x
1=-7,x
2=-
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.
分析:(1)移項,配方,開方,即可得出兩個一元一次方程,求出方程的解即可;
(2)分解因式,再開方,即可得出兩個一元一次方程,求出方程的解即可;
(3)分解因式,即可得出兩個一元一次方程,求出方程的解即可;
(4)移項后開方,即可得出兩個一元一次方程,求出方程的解即可.
點評:本題考查了解一元二次方程的應用,主要考查學生的計算能力.