COMPLETING THE SQUARE

The goal with completing the square is to create a perfect square trinomial.  These are trinomials that can be factored into a binomial squared such as the one below.

We usually have a squared term and a linear term and are asked to find what needs to be added to make a perfect square trinomial.  ALEKS states the problems as:

Find the value of d such that the expression below is a perfect square.

When the coefficient of the squared term is one (which it will be in this objective), then all we need to do is take half of the coefficient of the linear term, in this example -8, and square it.  Hence, the answer to this example is that d should be 16 because half of -8 is -4 and when we square -4, we get 16.

Notice this does indeed create a trinomial that factors into a binomial squared.

If the linear coefficient is odd we will get fractions, but that is not a problem.

Example:  Find d such that the expression below is a perfect square.

So d must equal .