Completing the Square - Problem 1

When you're doing your homework about completing the square the first few of your homework problems are probably going to look like this. They're going to ask you to make something into a perfect square trinomial and the way you do that is by taking half of this b term, squaring that value, by the way this is equal to 4. So I’m going to do 4² and that’s what’s going to go into my blank. I think that’s it.

I think I have a perfect square trinomial, let me just double check perfect square trinomial means it should look like this, (a+b)² equals a² plus 2ab plus b² let’s make sure that’s the case here. I have x² as my first term so I think a should be equal to x and then I have 16 as my b² value, so b should be equal to 4. I think (x+4)² is equal to this. If you were to go through and Foil it, you would see that indeed that’s correct x² plus 8x plus 16 can be written, rewritten as this perfect square binomial.

So let me just review with you what I did to get that 16. I took half of my b value which was 4 and then I squared it and wrote that here as my constant. That’s a really important process that you are going to be following through with your next homework problems.