For what real values of $c$ is $9x^2 + 16x + c$ the square of a binomial? If you find more than one, then list your values in increasing order, separated by commas.
9x^2 + 16x + c
A perfect square binomial will have one root
So...in the quadratic formula, we will have one root when the discriminant, b^2 - 4ac, equals 0....so....
16^2 - 4* 9 * c = 0
256 - 36c = 0 add 36 c to both sides
256 = 36c divide both sides by 36
64/9 = c