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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 66.9 = 0.5*((3865-25m)/(59-m)+(25m+2825)/(41+m)) .
    Question type: Equation
    Solution:Original question:
     
669
10
=
1
2
((386525 m ) ÷ (59 m ) + (25 m + 2825) ÷ (41 + m ))
    Remove a bracket on the right of the equation::
     
669
10
=
1
2
(386525 m ) ÷ (59 m ) +
1
2
(25 m + 2825) ÷ (41 + m )
     Multiply both sides of the equation by:(59 m )
     
669
10
(59 m ) =
1
2
(386525 m ) +
1
2
(25 m + 2825) ÷ (41 + m ) × (59 m )
    Remove a bracket on the left of the equation:
     
669
10
× 59
669
10
m =
1
2
(386525 m ) +
1
2
(25 m + 2825) ÷ (41 + m ) × (59 m )
    Remove a bracket on the right of the equation::
     
669
10
× 59
669
10
m =
1
2
× 3865
1
2
× 25 m +
1
2
(25 m + 2825) ÷ (41 + m ) × (59 m )
    The equation is reduced to :
     
39471
10
669
10
m =
3865
2
25
2
m +
1
2
(25 m + 2825) ÷ (41 + m ) × (59 m )
     Multiply both sides of the equation by:(41 + m )
     
39471
10
(41 + m )
669
10
m (41 + m ) =
3865
2
(41 + m )
25
2
m (41 + m ) +
1
2
(25 m + 2825)(59 m )
    Remove a bracket on the left of the equation:
     
39471
10
× 41 +
39471
10
m
669
10
m (41 + m ) =
3865
2
(41 + m )
25
2
m (41 + m ) +
1
2
(25 m + 2825)(59 m )
    Remove a bracket on the right of the equation::
     
39471
10
× 41 +
39471
10
m
669
10
m (41 + m ) =
3865
2
× 41 +
3865
2
m
25
2
m (41 + m ) +
1
2
(25 m + 2825)(59 m )
    The equation is reduced to :
     
1618311
10
+
39471
10
m
669
10
m (41 + m ) =
158465
2
+
3865
2
m
25
2
m (41 + m ) +
1
2
(25 m + 2825)(59 m )
    Remove a bracket on the left of the equation:
     
1618311
10
+
39471
10
m
669
10
m × 41
669
10
m m =
158465
2
+
3865
2
m
25
2
m (41 + m ) +
1
2
(25 m + 2825)(59 m )
    Remove a bracket on the right of the equation::
     
1618311
10
+
39471
10
m
669
10
m × 41
669
10
m m =
158465
2
+
3865
2
m
25
2
m × 41
25
2
m m +
1
2
(25 m + 2825)(59 m )
    The equation is reduced to :
     
1618311
10
+
39471
10
m
27429
10
m
669
10
m m =
158465
2
+
3865
2
m
1025
2
m
25
2
m m +
1
2
(25 m + 2825)(59 m )
    The equation is reduced to :
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+ 1420 m
25
2
m m +
1
2
(25 m + 2825)(59 m )
    Remove a bracket on the right of the equation::
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+ 1420 m
25
2
m m +
1
2
× 25 m (59 m ) +
1
2
× 2825
    The equation is reduced to :
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+ 1420 m
25
2
m m +
25
2
m (59 m ) +
2825
2
(59 m )
    Remove a bracket on the right of the equation::
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+ 1420 m
25
2
m m +
25
2
m × 59
25
2
m m
    The equation is reduced to :
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+ 1420 m
25
2
m m +
1475
2
m
25
2
m m +
2825
2
    The equation is reduced to :
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+
4315
2
m
25
2
m m
25
2
m m +
2825
2
(59 m )
    Remove a bracket on the right of the equation::
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+
4315
2
m
25
2
m m
25
2
m m +
2825
2
× 59
2825
2
    The equation is reduced to :
     
1618311
10
+
6021
5
m
669
10
m m =
158465
2
+
4315
2
m
25
2
m m
25
2
m m +
166675
2
2825
2
m
    The equation is reduced to :
     
1618311
10
+
6021
5
m
669
10
m m = 162570 + 745 m
25
2
m m
25
2
m m

    After the equation is converted into a general formula, there is a common factor:
    ( m - 9 )
    From
        m - 9 = 0

    it is concluded that::
        m1=9

    Solutions that cannot be obtained by factorization:
        m2≈1.959427 , keep 6 decimal places
    
    There are 2 solution(s).


解程的详细方法请参阅:《方程的解法》



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