Answer
{$-\frac{3\sqrt 2}{2}, \frac{3\sqrt 2}{2}$}.
Work Step by Step
Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain:
Step 1: $2x^{2}=9$
Step 2: $x^{2}=\frac{9}{2}$
Step 3: $x=\pm \sqrt {\frac{9}{2}}$
Step 4: $x=\pm \frac{\sqrt 9}{\sqrt 2}$
Step 5: $x=\pm \frac{3}{\sqrt 2}$
Step 6: $x=\pm \frac{3}{\sqrt 2}\times\frac{\sqrt 2}{\sqrt 2}$
Step 7: $x=\pm \frac{3\sqrt 2}{(\sqrt 2)^{2}}$
Step 8: $x=\pm \frac{3\sqrt 2}{2}$
The solution set is {$-\frac{3\sqrt 2}{2}, \frac{3\sqrt 2}{2}$}.
