Lulu has a quadratic of the form $x^2+bx+44$, where $b$ is a specific positive number. Using her knowledge of how to complete the square, Lulu is able to rewrite this quadratic in the form $(x+m)^2+8$. What is $b$?
I know that completing the square involves finding a constant term that makes the expression a perfect square trinomial, and then adding and subtracting that term to keep the expression equivalent. So, if Lulu started with $x^2+bx+44$ and ended up with $(x+m)^2+8$, she must have added and subtracted $(b/2)^2$ to the original expression. That means that $44-(b/2)^2=8$, since those are the constant terms of the two expressions. Solving for $b$, I get $(b/2)^2=36$, so $b/2=\pm 6$. But the problem said that $b$ is a positive number, so I can ignore the negative option and conclude that $b=12$. 