1. ## nonlinear inequalities #2

Sup again, thanks for catching my mistake. So this question wants me to solve the inequality and graph the solution on the real number line.

x^2+8x-5 ≥ 0

I couldn't factor it out so I went about using the quadratic equation and got
(-4 +√(42)), (-4-√(42))

I think im making a mistake somwhere

legend: √(…) is square root

hope i didnt make it too hard to read

2. Originally Posted by ugkwan
Sup again, thanks for catching my mistake. So this question wants me to solve the inequality and graph the solution on the real number line.

x^2+8x-5 ≥ 0

I couldn't factor it out so I went about using the quadratic equation and got
(-4 +√(42)), (-4-√(42))

I think im making a mistake somwhere

legend: √(…) is square root

hope i didnt make it too hard to read
$x=\frac{-8\pm\sqrt{64-4(-5)(1)}}{2}$

$=-4\pm\frac{\sqrt{84}}{2}$

I think you made a mistake here $\sqrt{84}=\sqrt{2}\sqrt{2}\sqrt{21}=2\sqrt{21}$

So your ordered pair should be:

$(-4+\sqrt{21},0),(-4-\sqrt{21},0)$

Those are the x-intercept points.

So now you have your test intervals:

$(-\infty,-4-\sqrt{21}),(-4-\sqrt{21},-4+\sqrt{21}),(-4+\sqrt{21},\infty)$

It might seem difficult to find test values, you just have to use your head here. Obviously $\sqrt{21}>\sqrt{16}=4$, so use something like that to help you find test values. You'll have to approximate to draw this on a number line though.