When the new SAT came out in March 2016, it became clear that the test makers were looking to test some skills that hadn’t appeared on the previous version of the test. One of those skills is “completing the square,” which can be helpful when you are working on problems involving circles and parabolas.

So what is completing the square? Well, a perfect square trinomial *x*²* + bx* + c is one that can be rewritten in the form (*x* + k)², where *k* is some integer. For instance *x*²* + *10*x* + 25 is a perfect square trinomial because is can be factored into (*x* + 5)(*x* + 5) = (*x* + 5)².

When you are asked to complete the square, you need to find that value of *c* (there is always only one possible value) that will make the trinomial a perfect square. For instance, suppose you were asked this question:

What number will complete the square for *x**² + *6*x + *___ ?