Here's an example.

Complete the square:

When completing the square, you have to think a little bit about what the left side of this equation looks like. You need to add something to the left side to make it a perfect square. A little bit of thought leads us to the conclusion that you need to have on the left side because that can be factored down to . We want to take all the constants on the left side over to the other side to give us a blank slate to work with on the left side.

Now, add 4 to both sides to "complete the square":

Factor.

The trickiest part is knowing what constant has to be added to the left side in order to "complete the square". You can figure it out by recognizing that the expansion of is . Since you know the middle term (2cy) corresponds to -4y, you know that . Cancel the y's and divide both sides by 2. . Since the third term in the expansion is , you know it must be +4. That's how you know it has to be .

That's about all there is to it. I hope this was clear enough...

Pulsar