Question

If using the method of completing the square to solve the quadratic equation

x2 - 6x + 6 = 0, which number would have to be added to "complete the square"?

Answer 1

Answer: 9

This is what the steps look like when we complete the square

x^2 - 6x + 6 = 0

x^2 - 6x = -6

x^2 - 6x + 9 = -6+9

(x-3)^2 = 3

We add 9 to both sides so that we can factor x^2-6x+9 into (x-3)(x-3) = (x-3)^2

To get the 9, we cut the -6 (from -6x) in half to get -6/2 = -3. Then we square that to get (-3)^2 = 9

It might help to look at (a+b)^2 = a^2+2ab+b^2 and note the relationship between 2ab and b^2.