Mathematics
         
语言：中文    Language:English
Equations   
Fold
Unary equation
Multivariate equation
Math OP  
Unfold
Linear algebra      
Unfold
Derivative function
Function image
Hot issues
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 (1+0.55x)(1+0.45x)(1+0.5x)(1+0.55x)(1+0.55x) = x+1 .
    Question type: Equation
    Solution:Original question:
     (1 +
11
20
 x )(1 +
9
20
 x )(1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x ) = x + 1
    Remove the bracket on the left of the equation:
     Left side of the equation = 1(1 +
9
20
 x )(1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x ) +
11
20
 x (1 +
9
20
 x )(1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x )
                                             = 1 × 1(1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x ) + 1 ×
9
20
 x (1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x ) +
11
20
                                             = 1(1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x ) +
9
20
 x (1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x ) +
11
20
 x (1 +
9
20
 x )
                                             = 1 × 1(1 +
11
20
 x )(1 +
11
20
 x ) + 1 ×
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x ) +
9
20
 x (1 +
1
2
 x )
                                             = 1(1 +
11
20
 x )(1 +
11
20
 x ) +
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x ) +
9
20
 x (1 +
1
2
 x )(1 +
11
20
 x )(1 +
11
20
 x )
                                             = 1 × 1(1 +
11
20
 x ) + 1 ×
11
20
 x (1 +
11
20
 x ) +
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x ) +
9
20
                                             = 1(1 +
11
20
 x ) +
11
20
 x (1 +
11
20
 x ) +
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x ) +
9
20
 x (1 +
1
2
 x )
                                             = 1 × 1 + 1 ×
11
20
 x +
11
20
 x (1 +
11
20
 x ) +
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x )
                                             = 1 +
11
20
 x +
11
20
 x (1 +
11
20
 x ) +
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x ) +
9
20
 x
                                             = 1 +
11
20
 x +
11
20
 x × 1 +
11
20
 x ×
11
20
 x +
1
2
 x
                                             = 1 +
11
20
 x +
11
20
 x +
121
400
 x x +
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x )
                                             = 1 +
11
10
 x +
121
400
 x x +
1
2
 x (1 +
11
20
 x )(1 +
11
20
 x ) +
9
20
 x
                                             = 1 +
11
10
 x +
121
400
 x x +
1
2
 x × 1(1 +
11
20
 x ) +
1
2
 x
                                             = 1 +
11
10
 x +
121
400
 x x +
1
2
 x (1 +
11
20
 x ) +
11
40
 x x
                                             = 1 +
11
10
 x +
121
400
 x x +
1
2
 x × 1 +
1
2
 x ×
11
20
                                             = 1 +
11
10
 x +
121
400
 x x +
1
2
 x +
11
40
 x x +
11
40
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x
                                             = 1 +
8
5
 x +
121
400
 x x +
11
40
 x x +
11
40
 x x

    After the equation is converted into a general formula, there is a common factor:
    ( x +0 )
    From
        x + 0 = 0
    it is concluded that:：
        x1=0

    Solutions that cannot be obtained by factorization:
        x2≈-4.405561 , keep 6 decimal places
        x3≈-0.970638 , keep 6 decimal places    
    There are 3 solution(s).

解程的详细方法请参阅：《方程的解法》


Your problem has not been solved here? Please go to the Hot Problems section！


Return



  New addition:Lenders ToolBox module（Specific location：Math OP > Lenders ToolBox ），welcome。