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