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On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    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 [(11+X)/(13+X)*50%]+[(10+X)/(13+X)*25%]+[(9+X)/(12+X)*25%] = 90% .
    Question type: Equation
    Solution:Original question:
     ((11 + X ) ÷ (13 + X ) ×
50
100
) + ((10 + X ) ÷ (13 + X ) ×
25
100
) + ((9 + X ) ÷ (12 + X ) ×
25
100
) =
90
100
    Remove a bracket on the left of the equation:：
     (11 + X ) ÷ (13 + X ) ×
50
100
 + ((10 + X ) ÷ (13 + X ) ×
25
100
) + ((9 + X ) ÷ (12 + X ) ×
25
100
) =
90
100
     Multiply both sides of the equation by:(13 + X )
     (11 + X ) ×
50
100
 + ((10 + X ) ÷ (13 + X ) ×
25
100
)(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X ) =
90
100
(13 + X )
    Remove a bracket on the left of the equation:
     11 ×
50
100
 + X ×
50
100
 + ((10 + X ) ÷ (13 + X ) ×
25
100
)(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X ) =
90
100
(13 + X )
    Remove a bracket on the right of the equation:：
     11 ×
50
100
 + X ×
50
100
 + ((10 + X ) ÷ (13 + X ) ×
25
100
)(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X ) =
90
100
 × 13 +
90
100
 X
    The equation is reduced to :
     
11
2
 + X ×
50
100
 + ((10 + X ) ÷ (13 + X ) ×
25
100
)(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X ) =
117
10
 +
90
100
 X
    Remove a bracket on the left of the equation:
     
11
2
 +
50
100
 X + (10 + X ) ÷ (13 + X ) ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X ) =
117
10
 +
90
100
 X
     Multiply both sides of the equation by:(13 + X )
     
11
2
(13 + X ) +
50
100
 X (13 + X ) + (10 + X ) ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X )(13 + X ) =
117
10
(13 + X ) +
90
100
 X (13 + X )
    Remove a bracket on the left of the equation:
     
11
2
 × 13 +
11
2
 X +
50
100
 X (13 + X ) + (10 + X ) ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X ) =
117
10
(13 + X ) +
90
100
 X (13 + X )
    Remove a bracket on the right of the equation:：
     
11
2
 × 13 +
11
2
 X +
50
100
 X (13 + X ) + (10 + X ) ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X ) =
117
10
 × 13 +
117
10
 X +
90
100
 X (13 + X )
    The equation is reduced to :
     
143
2
 +
11
2
 X +
50
100
 X (13 + X ) + (10 + X ) ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X )(13 + X ) =
1521
10
 +
117
10
 X +
90
100
 X (13 + X )
    Remove a bracket on the left of the equation:
     
143
2
 +
11
2
 X +
50
100
 X × 13 +
50
100
 X X + (10 + X ) ×
25
100
(13 + X ) =
1521
10
 +
117
10
 X +
90
100
 X (13 + X )
    Remove a bracket on the right of the equation:：
     
143
2
 +
11
2
 X +
50
100
 X × 13 +
50
100
 X X + (10 + X ) ×
25
100
(13 + X ) =
1521
10
 +
117
10
 X +
90
100
 X × 13 +
90
100
 X X
    The equation is reduced to :
     
143
2
 +
11
2
 X +
13
2
 X +
50
100
 X X + (10 + X ) ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
) =
1521
10
 +
117
10
 X +
117
10
 X +
90
100
 X X
    The equation is reduced to :
     
143
2
 + 12 X +
50
100
 X X + (10 + X ) ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X )(13 + X ) =
1521
10
 +
117
5
 X +
90
100
 X X
    Remove a bracket on the left of the equation:
     
143
2
 + 12 X +
50
100
 X X + 10 ×
25
100
(13 + X ) + X ×
25
100
(13 + X ) =
1521
10
 +
117
5
 X +
90
100
 X X
    The equation is reduced to :
     
143
2
 + 12 X +
50
100
 X X +
5
2
(13 + X ) + X ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
) =
1521
10
 +
117
5
 X +
90
100
 X X
    Remove a bracket on the left of the equation:
     
143
2
 + 12 X +
50
100
 X X +
5
2
 × 13 +
5
2
 X + X ×
25
100
 =
1521
10
 +
117
5
 X +
90
100
 X X
    The equation is reduced to :
     
143
2
 + 12 X +
50
100
 X X +
65
2
 +
5
2
 X + X ×
25
100
(13 + X ) =
1521
10
 +
117
5
 X +
90
100
 X X
    The equation is reduced to :
     104 +
29
2
 X +
50
100
 X X + X ×
25
100
(13 + X ) + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X )(13 + X ) =
1521
10
 +
117
5
 X +
90
100
 X X
    Remove a bracket on the left of the equation:
     104 +
29
2
 X +
50
100
 X X + X ×
25
100
 × 13 + X ×
25
100
 X =
1521
10
 +
117
5
 X +
90
100
 X X
    The equation is reduced to :
     104 +
29
2
 X +
50
100
 X X + X ×
13
4
 + X ×
25
100
 X + ((9 + X ) ÷ (12 + X ) ×
25
100
) =
1521
10
 +
117
5
 X +
90
100
 X X
    The equation is reduced to :
     104 +
71
4
 X +
50
100
 X X + X ×
25
100
 X + ((9 + X ) ÷ (12 + X ) ×
25
100
)(13 + X )(13 + X ) =
1521
10
 +
117
5
 X +
90
100
 X X
    Remove a bracket on the left of the equation:
     104 +
71
4
 X +
50
100
 X X + X ×
25
100
 X + (9 + X ) ÷ (12 + X ) ×
25
100
 =
1521
10
 +
117
5
 X +
90
100
 X X

    After the equation is converted into a general formula, it is converted into:
    ( √2X +√303 )( √2X - √303 )=0
    From
        √2X +√303 = 0
        √2X - √303 = 0
    it is concluded that:：
        X1=-
√303
√2
        X2=
√303
√2
    
    There are 2 solution(s).

解一元二次方程的详细方法请参阅：《一元二次方程的解法》


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