Me someone ! complete the square on the following quadratic

x^2+16x+9=0

what value is added to both sides of the equation.

Completing the square has us breaking rules of solving equations and factoring out the greatest common factor, but it is what it is! The first step is to make sure that the coefficient on the x^2 term is a 1 and it is so we are good there.  Now subtract 9 from both sides to get x^2 + 16x = -9. Complete the square on the left side by taking half of the linear term (16x) which is 8 and then squaring it to get 64.  That's what is added to both sides.  Now it looks like this:
x^2 + 16x + 64 = -9 + 64.  If you were to write it in vertex form it would look like this: (x+8)^2 - 55 = 0.  Now you can use this to plot the vertex of a parabola if you want to: it sits at (-8, -55)