Express x^2 - 7x + 2 in the form (x - p)^2 + q , where p and q are rational numbers.

This is an example of completing the square.If we expand (x - p)^2 + q, we will have x^2 -2px + p + q.Now we can use algebra to work out what p and q are from the following equation. x^2 - 7x + 2 = x^2 -2px + p^2 + q -7x + 2 = -2px + p^2 + q We can force an answer because 7x must equal to -2px so p = 7/2. Put p into the equation to get q. 7x + 2 = -27/2x + (7/2)^2 + q q = -41/4 so (x - 7/2)^2 -41/4