Solution - Radical equations

Radical Equation entered :

     √r+3 = r-3

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Radical already isolated
     √r+3 = r-3

Step  2  :

Eliminate the radical on the left hand side :

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

     After squaring
     r+3 = r²-6r+9

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     r²  - 7r  + 6 = 0

     This equation has two rational roots:
       {r1, r2}={6, 1}
 

Step  4  :

Check that the first solution is correct :

     Original equation
     √r+3 = r-3

     Plug in 6 for  r 
      √(6)+3 = (6)-3

      Simplify
      √9 = 3
      Solution checks !!
     Solution is:
      r = 6

Step  5  :

Check that the second solution is correct :

     Original equation
     √r+3 = r-3

     Plug in 1 for  r 
      √(1)+3 = (1)-3

      Simplify
      √4 = -2
      Solution does not check
      2 ≠ -2 

One solution was found :