Solution - Radical equations

Radical Equation entered :

     x = √54

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Original equation
     x = √54

     Isolate
     -√54 = -x

      Tidy up
     √54 = x

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√54)² = (x)²

     After squaring
     54 = x²

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x²  -54 = 0

     This equation has two real roots:
       x1 = ( 0 + sqrt(216) ) / 2 = 7.3485
      x2 = ( 0 - sqrt(216) ) / 2 = -7.3485

Step  4  :

Check that the first solution is correct :

     Original equation, root isolated, after tidy up
     √54 = x

     Plug in 7.3485 for  x 
      √54 = ( 7.3485)

      Simplify
      √54 = 7.348
      Solution checks !!
     Solution is:
      x =  7.3485

Step  5  :

Check that the second solution is correct :

     Original equation, root isolated, after tidy up
     √54 = x

     Plug in -7.3485 for  x 
      √54 = (-7.3485)

      Simplify
      √54 = -7.348
      Solution does not check
      7.348 ≠ -7.348 

One solution was found :