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

    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 39.5/(1.03+x)+31.65/[(1.03+x)(1.0714+x)]+24.28/[(1.03+x)(1.0714+x)(1.1516+x)]+17.38/[(1.03+x)(1.0714+x)(1.1516+x)(1.1282+x)] = 100 .
    Question type: Equation
    Solution:Original question:
     
79
2
÷ (
103
100
+ x ) +
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
869
50
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) = 100
     Multiply both sides of the equation by:(
103
100
+ x )
     
79
2
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) × (
103
100
+ x ) +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x ) +
869
50
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) × (
103
100
+ x ) = 100(
103
100
+ x )
    Remove a bracket on the left of the equation::
     
79
2
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) ×
103
100
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) × x +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x ) +
869
50
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) = 100(
103
100
+ x )
    Remove a bracket on the right of the equation::
     
79
2
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) ×
103
100
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) × x +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x ) +
869
50
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) = 100 ×
103
100
+ 100 x
    The equation is reduced to :
     
79
2
+
65199
2000
÷ ((
103
100
+ x )(
5357
5000
+ x )) +
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) × x +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x ) +
869
50
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) × (
103
100
+ x ) = 103 + 100 x
     Multiply both sides of the equation by:((
103
100
+ x )(
5357
5000
+ x ))
     
79
2
((
103
100
+ x )(
5357
5000
+ x )) +
65199
2000
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) × x ((
103
100
+ x )(
5357
5000
+ x )) +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
869
50
= 103((
103
100
+ x )(
5357
5000
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))
    Remove a bracket on the left of the equation:
     
79
2
(
103
100
+ x )(
5357
5000
+ x ) +
65199
2000
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) × x ((
103
100
+ x )(
5357
5000
+ x )) +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x )((
103
100
+ x )(
5357
5000
+ x )) = 103((
103
100
+ x )(
5357
5000
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))
    Remove a bracket on the right of the equation::
     
79
2
(
103
100
+ x )(
5357
5000
+ x ) +
65199
2000
+
633
20
÷ ((
103
100
+ x )(
5357
5000
+ x )) × x ((
103
100
+ x )(
5357
5000
+ x )) +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x )((
103
100
+ x )(
5357
5000
+ x )) = 103(
103
100
+ x )(
5357
5000
+ x ) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))
     Multiply both sides of the equation by:((
103
100
+ x )(
5357
5000
+ x ))
     
79
2
(
103
100
+ x )(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
65199
2000
((
103
100
+ x )(
5357
5000
+ x )) +
633
20
x ((
103
100
+ x )(
5357
5000
+ x )) +
607
25
÷ ((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) × (
103
100
+ x ) = 103(
103
100
+ x )(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x ))
    Remove a bracket on the left of the equation:
     
79
2
×
103
100
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
79
2
x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
65199
2000
((
103
100
+ x )(
5357
5000
+ x )) +
633
20
x = 103(
103
100
+ x )(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x ))
    Remove a bracket on the right of the equation::
     
79
2
×
103
100
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
79
2
x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
65199
2000
((
103
100
+ x )(
5357
5000
+ x )) +
633
20
x = 103 ×
103
100
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) + 103 x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x ))
    The equation is reduced to :
     
8137
200
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
79
2
x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) +
65199
2000
((
103
100
+ x )(
5357
5000
+ x )) +
633
20
x ((
103
100
+ x )(
5357
5000
+ x )) =
10609
100
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) + 103 x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x ))
     Multiply both sides of the equation by:((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x ))
     
8137
200
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
79
2
x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
65199
2000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) =
10609
100
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) + 103 x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))
    Remove a bracket on the left of the equation:
     
8137
200
×
5357
5000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
8137
200
x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
79
2
x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) =
10609
100
(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) + 103 x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) + 100 x ((
103
100
+ x )(
5357
5000
+ x ))
    Remove a bracket on the right of the equation::
     
8137
200
×
5357
5000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
8137
200
x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
79
2
x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )) =
10609
100
×
5357
5000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
10609
100
x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) + 103 x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))
    The equation is reduced to :
     
43589909
1000000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
8137
200
x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
79
2
x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) =
56832413
500000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) +
10609
100
x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )) + 103 x (
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x ))
     Multiply both sides of the equation by:((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x ))
     
43589909
1000000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) +
8137
200
x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) +
79
2
x (
5357
5000
+ x ) =
56832413
500000
((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) +
10609
100
x ((
103
100
+ x )(
5357
5000
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(
5641
5000
+ x )) + 103 x (
5357
5000
+ x )
    Remove a bracket on the left of the equation:
     
43589909
1000000
(
103
100
+ x )(
5357
5000
+ x )((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x ))((
103
100
+ x )(
5357
5000
+ x )(
2879
2500
+ x )(

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