What number must be placed in the blank below so that the resulting quadratic is the square of a binomial:
x^2 - 36x + __
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
Thank you!
c = (b/2)^2 = (-36/2)^2 = 324.
x^2 - 36x + 324 = (x-18)^2.
To find the number that must be placed in the blank so that the resulting quadratic is the square of a binomial, we can apply the concept of completing the square.
The square of a binomial has the form (x + a)^2, where 'a' is a constant.
We can start by writing the quadratic in the form of a perfect square trinomial:
x^2 - 36x + __ = (x - 18)^2
Let's expand this expression to verify if it matches the given quadratic:
(x - 18)^2 = x^2 - 36x + 324
By comparing the two expressions, we can see that the missing number in the blank is 324. Therefore, the quadratic that results in the square of a binomial is:
x^2 - 36x + 324.