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    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 177.7/（100+0.777x）+73.2/（100-0.268x）+31.4/（100-0.686x） = 1 .
    Question type: Equation
    Solution:Original question:
     
1777
10
 ÷ (100 +
777
1000
 x ) +
366
5
 ÷ (100 −
67
250
 x ) +
157
5
 ÷ (100 −
343
500
 x ) = 1
     Multiply both sides of the equation by:(100 +
777
1000
 x )
     
1777
10
 +
366
5
 ÷ (100 −
67
250
 x ) × (100 +
777
1000
 x ) +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x ) = 1(100 +
777
1000
 x )
    Remove a bracket on the left of the equation:：
     
1777
10
 +
366
5
 ÷ (100 −
67
250
 x ) × 100 +
366
5
 ÷ (100 −
67
250
 x ) ×
777
1000
 x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x ) = 1(100 +
777
1000
 x )
    Remove a bracket on the right of the equation:：
     
1777
10
 +
366
5
 ÷ (100 −
67
250
 x ) × 100 +
366
5
 ÷ (100 −
67
250
 x ) ×
777
1000
 x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x ) = 1 × 100 + 1 ×
777
1000
 x
    The equation is reduced to :
     
1777
10
 + 7320 ÷ (100 −
67
250
 x ) +
142191
2500
 ÷ (100 −
67
250
 x ) × x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x ) = 100 +
777
1000
 x
     Multiply both sides of the equation by:(100 −
67
250
 x )
     
1777
10
(100 −
67
250
 x ) + 7320 +
142191
2500
 x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x )(100 −
67
250
 x ) = 100(100 −
67
250
 x ) +
777
1000
 x (100 −
67
250
 x )
    Remove a bracket on the left of the equation:
     
1777
10
 × 100 −
1777
10
 ×
67
250
 x + 7320 +
142191
2500
 x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x )(100 −
67
250
 x ) = 100(100 −
67
250
 x ) +
777
1000
 x (100 −
67
250
 x )
    Remove a bracket on the right of the equation:：
     
1777
10
 × 100 −
1777
10
 ×
67
250
 x + 7320 +
142191
2500
 x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x )(100 −
67
250
 x ) = 100 × 100 − 100 ×
67
250
 x +
777
1000
 x (100 −
67
250
 x )
    The equation is reduced to :
     17770 −
119059
2500
 x + 7320 +
142191
2500
 x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x )(100 −
67
250
 x ) = 10000 −
134
5
 x +
777
1000
 x (100 −
67
250
 x )
    The equation is reduced to :
     25090 +
5783
625
 x +
157
5
 ÷ (100 −
343
500
 x ) × (100 +
777
1000
 x )(100 −
67
250
 x ) = 10000 −
134
5
 x +
777
1000
 x (100 −
67
250
 x )
     Multiply both sides of the equation by:(100 −
343
500
 x )
     25090(100 −
343
500
 x ) +
5783
625
 x (100 −
343
500
 x ) +
157
5
(100 +
777
1000
 x )(100 −
67
250
 x ) = 10000(100 −
343
500
 x ) −
134
5
 x (100 −
343
500
 x ) +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    Remove a bracket on the left of the equation:
     25090 × 100 − 25090 ×
343
500
 x +
5783
625
 x (100 −
343
500
 x ) +
157
5
(100 +
777
1000
 x )(100 −
67
250
 x ) = 10000(100 −
343
500
 x ) −
134
5
 x (100 −
343
500
 x ) +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    Remove a bracket on the right of the equation:：
     25090 × 100 − 25090 ×
343
500
 x +
5783
625
 x (100 −
343
500
 x ) +
157
5
(100 +
777
1000
 x )(100 −
67
250
 x ) = 10000 × 100 − 10000 ×
343
500
 x −
134
5
 x (100 −
343
500
 x ) +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    The equation is reduced to :
     2509000 −
860587
50
 x +
5783
625
 x (100 −
343
500
 x ) +
157
5
(100 +
777
1000
 x )(100 −
67
250
 x ) = 1000000 − 6860 x −
134
5
 x (100 −
343
500
 x ) +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    Remove a bracket on the left of the equation:
     2509000 −
860587
50
 x +
5783
625
 x × 100 −
5783
625
 x ×
343
500
 x +
157
5
(100 +
777
1000
 x ) = 1000000 − 6860 x −
134
5
 x (100 −
343
500
 x ) +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    Remove a bracket on the right of the equation:：
     2509000 −
860587
50
 x +
5783
625
 x × 100 −
5783
625
 x ×
343
500
 x +
157
5
(100 +
777
1000
 x ) = 1000000 − 6860 x −
134
5
 x × 100 +
134
5
 x ×
343
500
 x +
777
1000
 x
    The equation is reduced to :
     2509000 −
860587
50
 x +
23132
25
 x −
1983569
312500
 x x +
157
5
(100 +
777
1000
 x )(100 −
67
250
 x ) = 1000000 − 6860 x − 2680 x +
22981
1250
 x x +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    The equation is reduced to :
     2509000 −
814323
50
 x −
1983569
312500
 x x +
157
5
(100 +
777
1000
 x )(100 −
67
250
 x ) = 1000000 − 9540 x +
22981
1250
 x x +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    Remove a bracket on the left of the equation:
     2509000 −
814323
50
 x −
1983569
312500
 x x +
157
5
 × 100(100 −
67
250
 x ) +
157
5
 ×
777
1000
 x = 1000000 − 9540 x +
22981
1250
 x x +
777
1000
 x (100 −
67
250
 x )(100 −
343
500
 x )
    Remove a bracket on the right of the equation:：
     2509000 −
814323
50
 x −
1983569
312500
 x x +
157
5
 × 100(100 −
67
250
 x ) +
157
5
 ×
777
1000
 x = 1000000 − 9540 x +
22981
1250
 x x +
777
1000
 x × 100(100 −
343
500
 x ) −
777
1000
 x
    The equation is reduced to :
     2509000 −
814323
50
 x −
1983569
312500
 x x + 3140(100 −
67
250
 x ) +
121989
5000
 x (100 −
67
250
 x ) = 1000000 − 9540 x +
22981
1250
 x x +
777
10
 x (100 −
343
500
 x ) −
52059
250000
 x x
    Remove a bracket on the left of the equation:
     2509000 −
814323
50
 x −
1983569
312500
 x x + 3140 × 100 − 3140 ×
67
250
 x +
121989
5000
 = 1000000 − 9540 x +
22981
1250
 x x +
777
10
 x (100 −
343
500
 x ) −
52059
250000
 x x
    Remove a bracket on the right of the equation:：
     2509000 −
814323
50
 x −
1983569
312500
 x x + 3140 × 100 − 3140 ×
67
250
 x +
121989
5000
 = 1000000 − 9540 x +
22981
1250
 x x +
777
10
 x × 100 −
777
10
 x ×
343
500

    The solution of the equation:
        x1≈-128.700129 , keep 6 decimal places
        x2≈145.772595 , keep 6 decimal places
        x3≈184.604966 , keep 6 decimal places    
    There are 3 solution(s).

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