Solution - Radical equations

Radical Equation entered :

     √x+12-√x-9 = 3

Step by step solution :

Step  1  :

Isolate a square root on the left hand side :

     Original equation
     √x+12-√x-9 = 3

     Isolate
     √x+12 = √x-9+3

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√x+12)² = (√x-9+3)²

     After squaring
     x+12 = x-9+9+6√x-9

Step  3  :

Get remaining radical by itself :

     Current equation
     x+12 = x-9+9+6√x-9

     Isolate radical on the left hand side
     -6√x-9 = -x-12+x-9+9

      Tidy up
     6√x-9 = 12

Step  4  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (6√x-9)² = (12)²

     After squaring
     36x-324 = 144

Step  5  :

Solve the linear equation :

     Rearranged equation
      36x  -468 = 0

     Add  468  to both sides
      36x  = 468

     Divide both sides by 36
     A possible solution is :
     x = 13

Step  6  :

Check that the solution is correct :

     Original equation, root isolated, after tidy up
     √x+12 = √x-9+3

     Plug in 13 for  x 
      √(13)+12 = √(13)-9+3

      Simplify
      √25 = 5
      Solution checks !!
     Solution is:
      x = 13

One solution was found :