I need some help. I want to move on to Pre-Calculus Honors next year but in order to I have to learn extra stuff on my own, and pass a test. I'm doing okay but...

While checking an example problem's answer, I found something that I can't make sense of.

Here is what the question is.

A rectangle is 6 centimeters longer than it is wide. Find the dimensions if the area of the rectangle is more then 216sqcm.

I did it out, and went to check.

Here's what the packet said:

1. w(w+6)>216
2. w2 (that two means squared) + 6w> 216
3. w2+62-216>0
4. (w2 + 6w + 9) -216 -9>0
5. (w+3)2 (that two means squared) -225>0

Now its step 4 that makes me go o.0

I understand why they got nine, they're trying to complete the square...

BUT!

I don't understand why they are subtracting the nine. In order to get the last number in a completed square you do (b/2)2, so how did they get a negative nine? Isn't any number squared positive?

Help plz Dx