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On line Solution of Monovariate Equation：
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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 952 = 100÷（1+r）+100÷（（1+r）×（1+r））+1100÷（（1+r）×（1+r）×（1+r）） .
    Question type: Equation
    Solution:Original question:
     952 = 100 ÷ (1 + r ) + 100 ÷ ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r ))
     Multiply both sides of the equation by:(1 + r )
     952(1 + r ) = 100 + 100 ÷ ((1 + r )(1 + r )) × (1 + r ) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    Remove a bracket on the left of the equation:：
     952 × 1 + 952 r = 100 + 100 ÷ ((1 + r )(1 + r )) × (1 + r ) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    Remove a bracket on the right of the equation:：
     952 × 1 + 952 r = 100 + 100 ÷ ((1 + r )(1 + r )) × 1 + 100 ÷ ((1 + r )(1 + r )) × r + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    The equation is reduced to :
     952 + 952 r = 100 + 100 ÷ ((1 + r )(1 + r )) + 100 ÷ ((1 + r )(1 + r )) × r + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
     Multiply both sides of the equation by:((1 + r )(1 + r ))
     952((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r )) = 100((1 + r )(1 + r )) + 100 + 100 ÷ ((1 + r )(1 + r )) × r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )((1 + r )(1 + r ))
    Remove a bracket on the left of the equation:
     952(1 + r )(1 + r ) + 952 r ((1 + r )(1 + r )) = 100((1 + r )(1 + r )) + 100 + 100 ÷ ((1 + r )(1 + r )) × r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )((1 + r )(1 + r ))
    Remove a bracket on the right of the equation:：
     952(1 + r )(1 + r ) + 952 r ((1 + r )(1 + r )) = 100(1 + r )(1 + r ) + 100 + 100 ÷ ((1 + r )(1 + r )) × r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )((1 + r )(1 + r ))
     Multiply both sides of the equation by:((1 + r )(1 + r ))
     952(1 + r )(1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    Remove a bracket on the left of the equation:
     952 × 1(1 + r )((1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r ((1 + r )(1 + r )) + 1100 ÷ ((1 + r )(1 + r )(1 + r )) × (1 + r )
    Remove a bracket on the right of the equation:：
     952 × 1(1 + r )((1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100 × 1(1 + r )((1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r
    The equation is reduced to :
     952(1 + r )((1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )) = 100(1 + r )((1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )) + 100((1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))
     Multiply both sides of the equation by:((1 + r )(1 + r )(1 + r ))
     952(1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r )) = 100(1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    Remove a bracket on the left of the equation:
     952 × 1((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100(1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    Remove a bracket on the right of the equation:：
     952 × 1((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100 × 1((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))
    The equation is reduced to :
     952((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) = 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    Remove a bracket on the left of the equation:
     952(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    Remove a bracket on the right of the equation:：
     952(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))
    Remove a bracket on the left of the equation:
     952 × 1(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) = 100(1 + r )(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r ))
    Remove a bracket on the right of the equation:：
     952 × 1(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) = 100 × 1(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r ))
    The equation is reduced to :
     952(1 + r )((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 952 = 100(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100
    Remove a bracket on the left of the equation:
     952 × 1((1 + r )(1 + r )(1 + r )) + 952 r ((1 + r )(1 + r )(1 + r )) + 952 r (1 + r )((1 + r )(1 + r )(1 + r )) + 952 r = 100(1 + r )((1 + r )(1 + r )(1 + r )) + 100 r (1 + r )((1 + r )(1 + r )(1 + r )) + 100 r ((1 + r )(1 + r ))((1 + r )(1 + r )(1 + r )) + 100

    
        r≈0.119984 , keep 6 decimal places    
    There are 1 solution(s).

解一元一次方程的详细方法请参阅：《一元一次方程的解法》


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