Solution - Radical equations

Radical Equation entered :

     2+√x+8 = 3+√x-2

Step by step solution :

Step  1  :

Isolate a square root on the left hand side :

     Original equation
     2+√x+8 = 3+√x-2

     Isolate
     √x+8 = -2+3+√x-2

      Tidy up
     √x+8 = 1+√x-2

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√x+8)² = (1+√x-2)²

     After squaring
     x+8 = x-2+1+2√x-2

Step  3  :

Get remaining radical by itself :

     Current equation
     x+8 = x-2+1+2√x-2

     Isolate radical on the left hand side
     -2√x-2 = -x-8+x-2+1

      Tidy up
     2√x-2 = 9

Step  4  :

Eliminate the radical on the left hand side :

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

     After squaring
     4x-8 = 81

Step  5  :

Solve the linear equation :

     Rearranged equation
      4x  -89 = 0

     Add  89  to both sides
      4x  = 89

     Divide both sides by 4
     A possible solution is :
     x = (89/4)

Step  6  :

Check that the solution is correct :

     Original equation, root isolated, after tidy up
     √x+8 = 1+√x-2

     Plug in (89/4) for  x 
      √(89/4)+8 = 1+√(89/4)-2

      Simplify
      √30.25 = 5.5
      Solution checks !!
     Solution is:
      x = (89/4)

One solution was found :