Solution - Radical equations

Radical Equation entered :

     x-6 = √x-4

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Original equation
     x-6 = √x-4

     Isolate
     -√x-4 = -x+6

      Tidy up
     √x-4 = x-6

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√x-4)² = (x-6)²

     After squaring
     x-4 = x²-12x+36

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x²  - 13x  + 40 = 0

     This equation has two rational roots:
       {x1, x2}={8, 5}
 

Step  4  :

Check that the first solution is correct :

     Original equation, root isolated, after tidy up
     √x-4 = x-6

     Plug in 8 for  x 
      √(8)-4 = (8)-6

      Simplify
      √4 = 2
      Solution checks !!
     Solution is:
      x = 8

Step  5  :

Check that the second solution is correct :

     Original equation, root isolated, after tidy up
     √x-4 = x-6

     Plug in 5 for  x 
      √(5)-4 = (5)-6

      Simplify
      √1 = -1
      Solution does not check
      1 ≠ -1 

One solution was found :