Recall the algebraic identity
We can use this to complete the square. Consider the quadratic function
What can be added to yield a perfect square? Compare the coefficients of
: 
Then
Generalizing to any quadratic function of the form
, 2e=b which yields e=b/2. Hence
Example: Use Complete the Square Method to solve
Note that the method above is for quadratic functions containing
. We divide the equation by 2:
which is equivalent to
In order to generate a perfect square we add
to both sides of the equation
Easy algebraic calculations give
Taking the square-roots lead to
or
which give the solutions to the equation:
or 