Answer
{$7-3\sqrt 6,7+3\sqrt 6$}
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: $2(x-7)^{2}-7=101$
Step 2: $2(x-7)^{2}=101+7$
Step 3: $2(x-7)^{2}=108$
Step 4: $(x-7)^{2}=54$
Step 5: $x-7=\pm \sqrt {54}$
Step 6: $x-7=\pm \sqrt {9\times6}$
Step 7: $x-7=\pm 3\sqrt {6}$
Step 8: $x-7=3\sqrt 6$ or $x-7=-3\sqrt 6$
Step 9: $x=7+3\sqrt 6$ or $x=7-3\sqrt 6$
The solution set is {$7-3\sqrt 6,7+3\sqrt 6$}.
