Am I doing the perfect square trinomial correctly

Find c then factor it: x^2 + 7x + c
I know how to do it if the b is an even number.
I tried to figuring out the answer. Can you tell me if I'm doing it right? If not please tell me the correct way of doing it.

x^2 + 7x + c <----I divide the b or 7 by 1/2, then square the answer of 7/2 which you come up with 49/4
x^2 + 7x + 49 is it correct?
(x + 7/2)(x + 7/2) Did I factor it correctly?

Like you said, (7/2)^2 is 49/4, so it is x^2 + 7x + 49/4. But yes, that is correct.

Don't do things mechanically. Try to understand what you are to do and what you are doing.
You have not stated the complete question.
I suppose, the question is for what value of c the given expression is a perfect square ?
Proceed as follows :
x² + 7x + c [ Put it in the format a² ± 2 a b + b² so that it will be a perfect square = (a ± b)² ]
= x² + 2 * x * (7/2) + (7/2)² - (7/2)² + c [ add and subtract (7/2)² ]
= { x² + 2 * x * (7/2) + (7/2)²} - {(7/2)² - c}
= {x + (7/2)}² - {(7/2)² - c} = {x + (7/2)}²
[ If this is to be a perfect square then, {(7/2)² - c} = 0 => c = (7/2)² = 49/4 ]

yes