Solution - Radical equations

Radical Equation entered :

     √x-3+5 = x

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Original equation
     √x-3+5 = x

     Isolate
     √x-3 = -5+x

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√x-3)² = (-5+x)²

     After squaring
     x-3 = x²-10x+25

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x²  - 11x  + 28 = 0

     This equation has two rational roots:
       {x1, x2}={7, 4}
 

Step  4  :

Check that the first solution is correct :

     Original equation, root isolated
     √x-3 = -5+x

     Plug in 7 for  x 
      √(7)-3 = -5+(7)

      Simplify
      √4 = 2
      Solution checks !!
     Solution is:
      x = 7

Step  5  :

Check that the second solution is correct :

     Original equation, root isolated
     √x-3 = -5+x

     Plug in 4 for  x 
      √(4)-3 = -5+(4)

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

One solution was found :