To solve the inequality x^2 + 5x - 36 >= 0, we first need to find the factors of the quadratic equation x^2 + 5x - 36.

The factors are (x + 9)(x - 4).

Next, we need to find the values of x that satisfy the inequality. This can be done by setting each factor to zero and solving for x:

x + 9 = 0
x = -9

x - 4 = 0
x = 4

These values divide the number line into three intervals: (-∞, -9), (-9, 4), (4, ∞). We can then test values from each interval into the original inequality to determine which intervals satisfy the inequality.

For example, testing x = -10:

(-10)^2 + 5(-10) - 36 = 100 - 50 - 36 = 14

Since 14 is greater than or equal to 0, all values in the interval (-∞, -9) satisfy the inequality.

Testing x = 0:

0^2 + 5(0) - 36 = -36

Since -36 is not greater than or equal to 0, the interval (-9, 4) does not satisfy the inequality.

Testing x = 5:

5^2 + 5(5) - 36 = 25 + 25 - 36 = 14

Since 14 is greater than or equal to 0, all values in the interval (4, ∞) satisfy the inequality.

Therefore, the solution to the inequality x^2 + 5x - 36 >= 0 is x ≤ -9 or x ≥ 4.