What number must be placed in the blank below so that the resulting quadratic is the square of a binomial:

Question

x^2 - 36x + __

Answer 1

recall that (a+b)^2 = a^2 + 2ab + b^2
You have a^2 = x^2 so a=1
2ab = -36x
So, b = -18

x^2 - 36x + 324 = (x-18)^2

Answer 2

Thank you!

Answer 3

c = (b/2)^2 = (-36/2)^2 = 324.
x^2 - 36x + 324 = (x-18)^2.