Choice C is the correct answer. To complete the square for an expression $x^2 + bx$:

1. Take the coefficient of $x$, which is $b = 10$.
2. Divide it by 2: $10 / 2 = 5$.
3. Square the result: $5^2 = 25$.

So, $c = 25$. The expression becomes $x^2 + 10x + 25$, which factors to $(x + 5)^2$.

Choice A is incorrect because it is just $b$. Choice B is incorrect because it is $2b$. Choice D is incorrect because it is $b^2$.