Note that if you expand you get . Now look at the 'a' value in the 2ax term. That is your 'a' value in the expression.

So if you have a equation such as ... This can be re-written as and hence 3 is your 'a' value. So in this example completing the square would be...

since expanding gives so you need to take away a 3 from it to match your original equation.

Basically to generalize... If you have an equation of the form where n and m are some numbers, you should divide n by 2 to get the 'a' value in the equation .

So lets do your example...

Your n value is -4. Divide this by 2 to get -2. This is your 'a' value. Put this into the equation to get... .

Now expand this... . Since this is different from you original equation you need to subtract 9 to turn the +4 into a -9...

So your answer is! .