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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 4.6850 = ((28.02*0.639(x+0.1))/(1+0.639(x+0.1))*((100-6.66-1.14)/100)*(1/(1+0.31*1.14))+((0.76(x+0.1))/(1.3*0.101325)) ) .
    Question type: Equation
    Solution:Original question:
     
937
200
= ((
1401
50
×
639
1000
( x +
1
10
)) ÷ (1 +
639
1000
( x +
1
10
)) × ((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
)))
    Remove a bracket on the right of the equation::
     
937
200
= (
1401
50
×
639
1000
( x +
1
10
)) ÷ (1 +
639
1000
( x +
1
10
)) × ((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))
     Multiply both sides of the equation by:(1 +
639
1000
( x +
1
10
))
     
937
200
(1 +
639
1000
( x +
1
10
)) = (
1401
50
×
639
1000
( x +
1
10
))((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    Remove a bracket on the left of the equation:
     
937
200
× 1 +
937
200
×
639
1000
( x +
1
10
) = (
1401
50
×
639
1000
( x +
1
10
))((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    Remove a bracket on the right of the equation::
     
937
200
× 1 +
937
200
×
639
1000
( x +
1
10
) =
1401
50
×
639
1000
( x +
1
10
)((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    The equation is reduced to :
     
937
200
+
598743
200000
( x +
1
10
) =
895239
50000
( x +
1
10
)((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    Remove a bracket on the left of the equation:
     
937
200
+
598743
200000
x +
598743
200000
×
1
10
=
895239
50000
( x +
1
10
)((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    Remove a bracket on the right of the equation::
     
937
200
+
598743
200000
x +
598743
200000
×
1
10
=
895239
50000
x ((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) +
895239
50000
×
1
10
((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    The equation is reduced to :
     
937
200
+
598743
200000
x +
598743
2000000
=
895239
50000
x ((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) +
895239
500000
((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    The equation is reduced to :
     
9968743
2000000
+
598743
200000
x =
895239
50000
x ((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) +
895239
500000
((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    Remove a bracket on the right of the equation::
     
9968743
2000000
+
598743
200000
x =
895239
50000
x (100
333
50
57
50
) ÷ 100 × (1 ÷ (1 +
31
100
×
57
50
)) +
895239
500000
((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    The equation is reduced to :
     
9968743
2000000
+
598743
200000
x =
895239
5000000
x (100
333
50
57
50
)(1 ÷ (1 +
31
100
×
57
50
)) +
895239
500000
((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
)) + ((
19
25
( x +
1
10
)) ÷ (
13
10
×
4053
40000
))(1 +
639
1000
( x +
1
10
))
    Remove a bracket on the right of the equation::
     
9968743
2000000
+
598743
200000
x =
895239
5000000
x × 100(1 ÷ (1 +
31
100
×
57
50
))
895239
5000000
x ×
333
50
(1 ÷ (1 +
31
100
×
57
50
))
895239
5000000
x ×
57
50
(1 ÷ (1 +
31
100
×
57
50
))
    The equation is reduced to :
     
9968743
2000000
+
598743
200000
x =
895239
50000
x (1 ÷ (1 +
31
100
×
57
50
))
298114587
250000000
x (1 ÷ (1 +
31
100
×
57
50
))
51028623
250000000
x (1 ÷ (1 +
31
100
×
57
50
)) +
895239
500000
((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
))
    Remove a bracket on the right of the equation::
     
9968743
2000000
+
598743
200000
x =
895239
50000
x × 1 ÷ (1 +
31
100
×
57
50
)
298114587
250000000
x (1 ÷ (1 +
31
100
×
57
50
))
51028623
250000000
x (1 ÷ (1 +
31
100
×
57
50
)) +
895239
500000
((100
333
50
57
50
) ÷ 100)
    The equation is reduced to :
     
9968743
2000000
+
598743
200000
x =
895239
50000
x ÷ (1 +
31
100
×
57
50
)
298114587
250000000
x (1 ÷ (1 +
31
100
×
57
50
))
51028623
250000000
x (1 ÷ (1 +
31
100
×
57
50
)) +
895239
500000
((100
333
50
57
50
) ÷ 100)(1 ÷ (1 +
31
100
×
57
50
))
     Multiply both sides of the equation by:(1 +
31
100
×
57
50
)
     
9968743
2000000
(1 +
31
100
×
57
50
) +
598743
200000
x (1 +
31
100
×
57
50
) =
895239
50000
x
298114587
250000000
x (1 ÷ (1 +
31
100
×
57
50
))(1 +
31
100
×
57
50
)
51028623
250000000
x (1 ÷ (1 +
31
100
×
57
50
))(1 +
31
100
×
57
50
) +
895239
500000
((100
333
50
57
50
) ÷ 100)
    Remove a bracket on the left of the equation:
     
9968743
2000000
× 1 +
9968743
2000000
×
31
100
×
57
50
+
598743
200000
x (1 +
31
100
×
57
50
) =
895239
50000
x
298114587
250000000
x (1 ÷ (1 +
31
100
×
57
50
))(1 +
31
100
×
57
50
)
51028623
250000000
x (1 ÷ (1 +
31
100
×
57
50
))(1 +
31
100
×
57
50
) +
895239
500000
((100
333
50
57
50
) ÷ 100)
    Remove a bracket on the right of the equation::
     
9968743
2000000
× 1 +
9968743
2000000
×
31
100
×
57
50
+
598743
200000
x (1 +
31
100
×
57
50
) =
895239
50000
x
298114587
250000000
x × 1 ÷ (1 +
31
100
×
57
50
) × (1 +
31
100
×
57
50
)
51028623
250000000
x (1 ÷ (1 +
31
100
×
57
50
))(1 +
31
100
×
57
50
) +
895239
500000

    The solution of the equation:
        x1≈-1.664945 , keep 6 decimal places
        x2≈0.409025 , keep 6 decimal places
    
    There are 2 solution(s).


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