Question: If f(x) = x^2 + 5x + c and f(3) = 0, find the value of c. Enter your numeric value (do NOT enter the variable).
1. **State the problem:** We are given a quadratic function $$f(x) = x^2 + 5x + c$$ and told that $$f(3) = 0$$. We need to find the value of $$c$$.
2. **Write the formula and substitute:** Since $$f(3) = 0$$, substitute $$x = 3$$ into the function:
$$f(3) = 3^2 + 5(3) + c = 0$$
3. **Calculate the known terms:**
$$3^2 = 9$$
$$5(3) = 15$$
So the equation becomes:
$$9 + 15 + c = 0$$
4. **Simplify the equation:**
$$24 + c = 0$$
5. **Solve for $$c$$:**
$$c = -24$$
**Final answer:** $$c = -24$$