We are given the inequality:
x2+6x<91.Rearranging the inequality:
x2+6x−91<0.Now, solve the corresponding equation:
x2+6x−91=0.We can solve this using the quadratic formula:
x=‌, where
a=1,b=6, and
c=−91. Substituting these values:
Thus, the two roots are:
x=‌=7,‌‌x=‌=−13.
The inequality
x2+6x−91<0 holds between the roots, so the solution set is:
{x:−13<x<7}. Quick Tip
To solve quadratic inequalities, first solve the corresponding quadratic equation,
then test the intervals formed by the roots.