Quadratic match

If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value
of c?
(1) d = 3
(2) b = 6


Is it possible to look at it from this point of view.

Taking statement 1 Alone:
d=3

x^2 + bx + c = (x + d)^2 , d=3
x^2 + bx + c = (x + 3)^2
expanding the RHS and comparing coefficients, it is possible to determine c

So 1 is sufficient.

Taking statement 2
b = 6
x^2 + bx + c = (x + d)^2

x^2 + 6x + c = (x + d)^2
x^2 + 6x + c = x^2 + 2dx + d^2

comparing coefficients,

2d=6
d=3

c= d^2
c= (3)^2
c=9

Statement 2 is Sufficient.

But we know by comparing the two sides that c=d^2 and Statement one provides us with the value of d=3.

Therefore, c=d^2=(3)^2=9

Hence, Statement 1 is sufficient.