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