Solution - Radical equations

Radical Equation entered :

     √x-95+√x = 19

Step by step solution :

Step  1  :

Isolate a square root on the left hand side :

     Original equation
     √x-95+√x = 19

     Isolate
     √x-95 = -√x+19

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√x-95)² = (-√x+19)²

     After squaring
     x-95 = x+361-38√x

Step  3  :

Get remaining radical by itself :

     Current equation
     x-95 = x+361-38√x

     Isolate radical on the left hand side
     38√x = -x+95+x+361

      Tidy up
     38√x = 456

Step  4  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (38√x)² = (456)²

     After squaring
     1444x = 207936

Step  5  :

Solve the linear equation :

     Rearranged equation
      1444x  -207936 = 0

     Add  207936  to both sides
      1444x  = 207936

     Divide both sides by 1444
     A possible solution is :
     x = 144

Step  6  :

Check that the solution is correct :

     Original equation, root isolated, after tidy up
     √x-95 = -√x+19

     Plug in 144 for  x 
      √(144)-95 = -√(144)+19

      Simplify
      √49 = 7
      Solution checks !!
     Solution is:
      x = 144

One solution was found :