The simplest way to solve an inequality like this, , or one more complicated, is to solve the correspondingequation, . That can be solved by completing the square or by using the quadratic formula.

The point is that a continuous function, such as this, can change from "> 0" to "< 0" only where it is equal to 0.

Those two points, and divides the number line into three intervals:

Choose one point in each interval: since [tex]2\sqrt{2}[/itex] is between 2 and 3, is between -5/2 and 1/2. -3 is in the first interval and 0 is in the second.

so every does not satisify the inequality.

so every satifies the inequality.

x= 2 is in the last interval and so any does not satisfy the inequality.

The inequality is satisfied for .

Of course, for this simple inequality, that is exactly the same as saying that the graph of [tex]y= x^2+ 2x- 1[/itex] is a parabola opening upward and so y< 0 for x between the two x-intercepts.