Find the value of b that makes a perfect square trinomial

Perfect square trinomial is like

(x+4)^2=x^2+8x+16
they are represented as such
ax^2+bx+c
so to solve for b you do
(√c) times 2=b so

c=9/4
square root=3/2 because 3/2 times 3/2=9/4
(√(9/4)) times 2=(3/2) times 2=6/2=3
so b=3

x^2+3x+(9/4)
if factored, it gives
(x+(3/2))(x+(3/2))  or
(x-(3/2))(x-(3/2))

if this equation is equal to 0 then x=-3/2 or 3/2

the value is 3

The last answer choice