Completing the square is a process that has several steps. usually, students learn some of the components of this process separately, prior to putting them all together to complete the square. what are some of the key components of this process?

Here's an example of completing the square:

4X² + 12X -16 = 0

1) Move the "non X" term to the right

4X² + 12X = 16


2) Divide the equation by the coefficient of X² which in this case is 4
so the equation becomes:
 X² + 3X = 43) Now here's the "completing the square" stage in which we:      • take the coefficient of X
      • divide it by 2
      • square that number
      • then add it to both sides of the equation.

In our sample problem
      the coefficient of X is 3
      dividing this by 2 equals 1.5
      squaring this number equals (1.5)² = 2.25
      Now, adding that to both sides of the equation, we have:
X² + 3X + 2.25 = 4 + 2.254) Finally, we can take the square root of both sides of the equation and we have:
X + 1.5 = Square Root (4 + 2.25)
X = Square Root (6.25) -1.5
X = 2.5 -1.5
X = 1.0
Let's not forget that the other square root of 6.25 is -2.5 and so the other root of the equation is:
(-2.5 -1.5) = -4

Source:
http://www.1728.org/quadr2.htm