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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.
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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+(k*k)]*{[12-8(k*k)]/{[1-2(k*k)]*[1-2(k*k)]}} = 60 .
    Question type: Equation
    Solution:Original question:
     (1 + ( k k ))((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k )))) = 60
    Remove a bracket on the left of the equation:：
     1((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k )))) + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k )))) = 60
    Remove a bracket on the left of the equation:
     1(12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))) + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k )))) = 60
     Multiply both sides of the equation by:((1 − 2( k k ))(1 − 2( k k )))
     1(12 − 8( k k )) + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60((1 − 2( k k ))(1 − 2( k k )))
    Remove a bracket on the left of the equation:
     1 × 12 − 1 × 8( k k ) + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60((1 − 2( k k ))(1 − 2( k k )))
    Remove a bracket on the right of the equation:：
     1 × 12 − 1 × 8( k k ) + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60(1 − 2( k k ))(1 − 2( k k ))
    The equation is reduced to :
     12 − 8( k k ) + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60(1 − 2( k k ))(1 − 2( k k ))
    Remove a bracket on the left of the equation:
     12 − 8 k k + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60(1 − 2( k k ))(1 − 2( k k ))
    Remove a bracket on the right of the equation:：
     12 − 8 k k + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60 × 1(1 − 2( k k )) − 60 × 2( k k )(1 − 2( k k ))
    The equation is reduced to :
     12 − 8 k k + ( k k )((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60(1 − 2( k k )) − 120( k k )(1 − 2( k k ))
    Remove a bracket on the left of the equation:
     12 − 8 k k + k k ((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60(1 − 2( k k )) − 120( k k )(1 − 2( k k ))
    Remove a bracket on the right of the equation:：
     12 − 8 k k + k k ((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60 × 1 − 60 × 2( k k ) − 120( k k )(1 − 2( k k ))
    The equation is reduced to :
     12 − 8 k k + k k ((12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))))((1 − 2( k k ))(1 − 2( k k ))) = 60 − 120( k k ) − 120( k k )(1 − 2( k k ))
    Remove a bracket on the left of the equation:
     12 − 8 k k + k k (12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))) × ((1 − 2( k k ))(1 − 2( k k ))) = 60 − 120( k k ) − 120( k k )(1 − 2( k k ))
    Remove a bracket on the right of the equation:：
     12 − 8 k k + k k (12 − 8( k k )) ÷ ((1 − 2( k k ))(1 − 2( k k ))) × ((1 − 2( k k ))(1 − 2( k k ))) = 60 − 120 k k − 120( k k )(1 − 2( k k ))
     Multiply both sides of the equation by:((1 − 2( k k ))(1 − 2( k k )))
     12((1 − 2( k k ))(1 − 2( k k ))) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) + k k (12 − 8( k k ))((1 − 2( k k ))(1 − 2( k k ))) = 60((1 − 2( k k ))(1 − 2( k k ))) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120( k k )(1 − 2( k k ))((1 − 2( k k ))(1 − 2( k k )))
    Remove a bracket on the left of the equation:
     12(1 − 2( k k ))(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) + k k (12 − 8( k k ))((1 − 2( k k ))(1 − 2( k k ))) = 60((1 − 2( k k ))(1 − 2( k k ))) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120( k k )(1 − 2( k k ))((1 − 2( k k ))(1 − 2( k k )))
    Remove a bracket on the right of the equation:：
     12(1 − 2( k k ))(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) + k k (12 − 8( k k ))((1 − 2( k k ))(1 − 2( k k ))) = 60(1 − 2( k k ))(1 − 2( k k )) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120( k k )(1 − 2( k k ))((1 − 2( k k ))(1 − 2( k k )))
    Remove a bracket on the left of the equation:
     12 × 1(1 − 2( k k )) − 12 × 2( k k )(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) + k = 60(1 − 2( k k ))(1 − 2( k k )) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120( k k )(1 − 2( k k ))((1 − 2( k k ))(1 − 2( k k )))
    Remove a bracket on the right of the equation:：
     12 × 1(1 − 2( k k )) − 12 × 2( k k )(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) + k = 60 × 1(1 − 2( k k )) − 60 × 2( k k )(1 − 2( k k )) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120
    The equation is reduced to :
     12(1 − 2( k k )) − 24( k k )(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) + k k (12 − 8( k k )) = 60(1 − 2( k k )) − 120( k k )(1 − 2( k k )) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120( k k )(1 − 2( k k ))
    Remove a bracket on the left of the equation:
     12 × 1 − 12 × 2( k k ) − 24( k k )(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) = 60(1 − 2( k k )) − 120( k k )(1 − 2( k k )) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120( k k )(1 − 2( k k ))
    Remove a bracket on the right of the equation:：
     12 × 1 − 12 × 2( k k ) − 24( k k )(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) = 60 × 1 − 60 × 2( k k ) − 120( k k )(1 − 2( k k )) − 120 k k ((1 − 2( k k ))(1 − 2( k k )))
    The equation is reduced to :
     12 − 24( k k ) − 24( k k )(1 − 2( k k )) − 8 k k ((1 − 2( k k ))(1 − 2( k k ))) + k k = 60 − 120( k k ) − 120( k k )(1 − 2( k k )) − 120 k k ((1 − 2( k k ))(1 − 2( k k ))) − 120( k k )

    The solution of the equation:
        k1≈-0.843833 , keep 6 decimal places
        k2≈-0.521361 , keep 6 decimal places
        k3≈0.521361 , keep 6 decimal places
        k4≈0.843833 , keep 6 decimal places    
    There are 4 solution(s).

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