Start like this: x^2 - 6x = -7. Now you have the x terms on one side and the constant on the other. Take half the linear term (-6x) which is 3 and then square that (9) and add it to both sides, giving you x^2 - 6x + 9 = -7+ 9, or x^2 - 6x + 9 = 2. Now make the left side into the perfect square binomial you created by completing the square: (x-3)^2 = 2, and then move the 2 over to get: (x-3)^2 - 2. That's the vertex form for a parabola with a vertex at (3, -2)
