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=2a−b±b2−4ac, where a=1,b=6, and c=−91. Substituting these values:
Thus, the two roots are:x=2−6+20=7,x=2−6−20=−13. The inequality x2+6x−91<0 holds between the roots, so the solution set is:{x:−13<x<7}. Quick TipTo solve quadratic inequalities, first solve the corresponding quadratic equation,then test the intervals formed by the roots.