For the function $f(x)=x^{2}+5 x-36$ solve the following.
\[
f(x) \leq 0
\]
Select the correct choice below and fill in the answer box within your choice.
A. The solution is (Use a comma to separate answers as needed.)
B. The solution is
(Type your answer in interval notation.)

Answer

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Answer

Thus, the solution is $x \in \boxed{[-9,4]}$.

Steps

Step 1 ：Factor the quadratic expression on the left side of the inequality, which gives $(x - 4)(x + 9)$.

Step 2 ：Build a sign chart to determine the signs of the factors and the product in different intervals.

Step 3 ：From the sign chart, we can see that $x^2 + 5x - 36$ is less than or equal to 0 when $-9 < x < 4$.

Step 4 ：Also, $f(x) = 0$ at $x = 4$ and $x = -9$.

Step 5 ：Thus, the solution is $x \in \boxed{[-9,4]}$.