Answer
{$-3\sqrt 2, 3\sqrt 2$}
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: $3x^{2}-54=0$
Step 2: $3x^{2}=54$
Step 3: $x^{2}=\frac{54}{3}$
Step 4: $x^{2}=18$
Step 5: $x=\pm \sqrt {18}$
Step 6: $x=\pm \sqrt {9\times 2}$
Step 7: $x=\pm (\sqrt {9}\times \sqrt 2)$
Step 8: $x=\pm (3\times \sqrt 2)$
Step 9: $x=\pm 3\sqrt 2$
The solution set is {$-3\sqrt 2, 3\sqrt 2$}.
