Solution - Radical equations

Radical Equation entered :

     √x = 12-x+32

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Radical already isolated
     √x = 12-x+32

      Tidy up
     √x = 44-x

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√x)² = (44-x)²

     After squaring
     x = x²-88x+1936

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x²  - 89x  + 1936 = 0

     This equation has two real roots:
       x1 = ( 89 + sqrt(177) ) / 2 = 51.1521
      x2 = ( 89 - sqrt(177) ) / 2 = 37.8479

Step  4  :

Check that the first solution is correct :

     Original equation, after tidy up
     √x = 44-x

     Plug in 51.1521 for  x 
      √(51.1521)  = 44-(51.1521)

      Simplify
      √51.152 = -7.152
      Solution does not check
      7.152 ≠ -7.152 

Step  5  :

Check that the second solution is correct :

     Original equation, after tidy up
     √x = 44-x

     Plug in 37.8479 for  x 
      √(37.8479)  = 44-(37.8479)

      Simplify
      √37.848 = 6.152
      Solution checks !!
     Solution is:
      x = 37.8479

One solution was found :