Maximizing the function f(X)=6X-1/2X^2+82. That's it, so 6X-1/2X^2+82 = 82-1/2(X^2-12X) = 82-1/2(X-6)^2+18. So f(X)=100-1/2(X-6)^2. Since (X-6)^2 is positive for any X not =6, than the max is x=6. The part I don't understand is when rearranging the function, how do you get from -1/2(X^2-12X) to -1/2(X-6)^2+18?
The focus of the problem assumes my question is already common knowledge, so I don't think there are any relevant equations.
The Attempt at a Solution
Not sure what to do, at first I worked backwards trying to expand (x-6)^2+18, which is X^2-12X+54, but I'm at a dead end. This isn't actually for a class, but thanks for your help in advance!