Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial.
x^2 + 8x + ____
Well, we can say it is (x+y)^2 which expanded is x^2+2xy+y^2. We can see in the original equation it is x^2 which is in our expanded equation and then 8x is 2xy in the expanded equation. This means that 2xy=8x, or y=4. This means the blank which is y^2 is 4^2 or 16.
So the constant is 16 and the equation is x^2+8x+16.