Solution - Radical equations

Radical Equation entered :

     x-√2x+5 = 5

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Original equation
     x-√2x+5 = 5

     Isolate
     -√2x+5 = -x+5

      Tidy up
     √2x+5 = x-5

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√2x+5)² = (x-5)²

     After squaring
     2x+5 = x²-10x+25

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x²  - 12x  + 20 = 0

     This equation has two rational roots:
       {x1, x2}={10, 2}
 

Step  4  :

Check that the first solution is correct :

     Original equation, root isolated, after tidy up
     √2x+5 = x-5

     Plug in 10 for  x 
      √2•(10)+5 = (10)-5

      Simplify
      √25 = 5
      Solution checks !!
     Solution is:
      x = 10

Step  5  :

Check that the second solution is correct :

     Original equation, root isolated, after tidy up
     √2x+5 = x-5

     Plug in 2 for  x 
      √2•(2)+5 = (2)-5

      Simplify
      √9 = -3
      Solution does not check
      3 ≠ -3 

One solution was found :