To solve the inequality x^2 + 7x - 2 < -12, we can follow these steps:
1. Begin by subtracting -12 from both sides of the inequality to isolate the quadratic expression on the left side:
x^2 + 7x - 2 + 12 < 0
2. Combine like terms:
x^2 + 7x + 10 < 0
3. Now, we need to factorize the quadratic expression on the left side:
(x + 5)(x + 2) < 0
4. To determine the values of x that satisfy the inequality, we can analyze the sign changes in the expression:
-5 < x < -2
Therefore, the solution to the inequality x^2 + 7x - 2 < -12 is -5 < x < -2.