Answer
$-1+\displaystyle \frac{\sqrt{22}}{2}$ and $-1-\displaystyle \frac{\sqrt{22}}{2}$
are to be excluded from the domain
Work Step by Step
Excluded from the domain are all values of x that yield 0 in the denominator.
These values are solutions of
$2x^{2}+4x-9=0 \; $... apply the quadratic formula
$ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-4\pm\sqrt{4^{2}-4(2)(-9)}}{2a}$
$=\displaystyle \frac{-4\pm\sqrt{88}}{4}=\frac{-4\pm 2\sqrt{22}}{4}$
$=\displaystyle \frac{2(-2\pm\sqrt{22})}{4}=\frac{-2\pm\sqrt{22}}{2}$
$-1+\displaystyle \frac{\sqrt{22}}{2}$ and $-1-\displaystyle \frac{\sqrt{22}}{2}$
are to be excluded from the domain
