# Week 6 – Precalc 11

This week in precalc 11 we learned how to use the zero product law, which just simply means that if ab = 0, then either a = 0 or b = 0, or both. Let’s say for example we have $x^2$ + x – 30 = 0. First we factor the left side, ( x + 6 ) (x – 5 ) = 0 , now we use the zero product law, being x + 6 = 0 ,  and x – 5 = 0. Now we just simply solve this like any other equation and isolate X, and the final answer is either x = – 6 or x = 5 (these are the two solutions of the equation)

We also learned how to use square roots to solve quadratic equations, also called completing the square. This usually happens when the equation doesn’t factor, but luckily there are 3 steps you can use to do so. First, you take the middle term, then you divide it in half and finally, you square it.

Let’s say for example, we have $x^2$ + 6x + __

First we identify the middle term, which is 6x. Then we divide it in half, giving us 3, and then you just square it, giving us 9.  At the end, the whole equation looks like this:

$x^2$ + 6x + 9