Answer
$=2\sqrt{17}$
$\approx 8.25$
Work Step by Step
The given function is
$=\sqrt{b^2-4ac}$
Substitute $-2$ for $a,8$ for $b,$ and $\frac{1}{2}$ for $c$.
$=\sqrt{(8)^2-4(-2)(\frac{1}{2})}$
Simplify.
$=\sqrt{64+4}$
$=\sqrt{68}$
Factor as square term.
$=\sqrt{4\cdot 17}$
$=\sqrt{2^2\cdot 17}$
Use product property of square roots.
$=\sqrt{2^2}\cdot \sqrt{17}$
Simplify.
$=2\sqrt{17}$
Rounded to the nearest hundredth.
$\approx 8.25$
