Find a such that ax^2+15x+9 is the square of a binomial.
(sqrta x +3)^2 = ax^2 + 15x + 9 expand the binomial on the L side
ax^2 + 6 sqrt a + 9 = ax^2 + 15x + 9
so 6sqrt a = 15
sqrt a = 2.5
a = 6.25