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On line Solution of Monovariate Equation：
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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 1+x = (1+0.6*x)*(1+0.5*x)*(1+0.2*x)*(1+0.2*x)*(1+0.2*x)*(1+0.2*x) .
    Question type: Equation
    Solution:Original question:
     1 + x = (1 +
3
5
 x )(1 +
1
2
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )
    Remove the bracket on the right of the equation:
     Right side of the equation = 1(1 +
1
2
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) +
3
5
 x (1 +
1
2
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )
                                               = 1 × 1(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) + 1 ×
1
2
 x (1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )
                                               = 1(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) +
1
2
 x (1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) +
3
5
                                               = 1 × 1(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) + 1 ×
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) +
1
2
                                               = 1(1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x ) +
1
2
 x (1 +
1
5
 x )
                                               = 1 × 1(1 +
1
5
 x )(1 +
1
5
 x ) + 1 ×
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )
                                               = 1(1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x )(1 +
1
5
 x )
                                               = 1 × 1(1 +
1
5
 x ) + 1 ×
1
5
 x (1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
                                               = 1(1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )
                                               = 1 × 1 + 1 ×
1
5
 x +
1
5
 x (1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x )
                                               = 1 +
1
5
 x +
1
5
 x (1 +
1
5
 x ) +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
 x
                                               = 1 +
1
5
 x +
1
5
 x × 1 +
1
5
 x ×
1
5
 x +
1
5
 x
                                               = 1 +
1
5
 x +
1
5
 x +
1
25
 x x +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x )
                                               = 1 +
2
5
 x +
1
25
 x x +
1
5
 x (1 +
1
5
 x )(1 +
1
5
 x ) +
1
5
 x
                                               = 1 +
2
5
 x +
1
25
 x x +
1
5
 x × 1(1 +
1
5
 x ) +
1
5
 x
                                               = 1 +
2
5
 x +
1
25
 x x +
1
5
 x (1 +
1
5
 x ) +
1
25
 x x
                                               = 1 +
2
5
 x +
1
25
 x x +
1
5
 x × 1 +
1
5
 x ×
1
5
                                               = 1 +
2
5
 x +
1
25
 x x +
1
5
 x +
1
25
 x x +
1
25
                                               = 1 +
3
5
 x +
1
25
 x x +
1
25
 x x +
1
25
 x x
                                               = 1 +
3
5
 x +
1
25
 x x +
1
25
 x x +
1
25
 x x
                                               = 1 +
3
5
 x +
1
25
 x x +
1
25
 x x +
1
25
 x x
                                               = 1 +
3
5
 x +
1
25
 x x +
1
25
 x x +
1
25
 x x
                                               = 1 +
3
5
 x +
1
25
 x x +
1
25
 x x +
1
25
 x x
                                               = 1 +
3
5
 x +
1
25
 x x +
1
25
 x x +
1
25
 x x
                                               = 1 +
3
5
 x +
1
25
 x x +
1
25
 x x +
1
25
 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≈-0.876994 , keep 6 decimal places    
    There are 2 solution(s).

解程的详细方法请参阅：《方程的解法》


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