Solution - Radical equations

Radical Equation entered :

     √4m+29-m = 2

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Original equation
     √4m+29-m = 2

     Isolate
     √4m+29 = m+2

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√4m+29)² = (m+2)²

     After squaring
     4m+29 = m²+4m+4

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     m²  -25 = 0

     This equation has two rational roots:
       {m1, m2}={5, -5}
 

Step  4  :

Check that the first solution is correct :

     Original equation, root isolated
     √4m+29 = m+2

     Plug in 5 for  m 
      √4•(5)+29 = (5)+2

      Simplify
      √49 = 7
      Solution checks !!
     Solution is:
      m = 5

Step  5  :

Check that the second solution is correct :

     Original equation, root isolated
     √4m+29 = m+2

     Plug in  -5 for  m 
      √4•(-5)+29 = (-5)+2

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

One solution was found :