Answer
{$-3\sqrt 3, 3\sqrt 3$}
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: $4x^{2}-108=0$
Step 2: $4x^{2}=108$
Step 3: $x^{2}=\frac{108}{4}$
Step 4: $x^{2}=27$
Step 5: $x=\pm \sqrt {27}$
Step 6: $x=\pm \sqrt {9\times 3}$
Step 7: $x=\pm (\sqrt {9}\times \sqrt 3)$
Step 8: $x=\pm (3\times \sqrt 3)$
Step 9: $x=\pm 3\sqrt 3$
The solution set is {$-3\sqrt 3, 3\sqrt 3$}.
