Answer
{$-8-5\sqrt 2,-8+5\sqrt 2$}
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: $2(x+8)^{2}-9=91$
Step 2: $2(x+8)^{2}=91+9$
Step 3: $2(x+8)^{2}=100$
Step 4: $(x+8)^{2}=50$
Step 5: $x+8=\pm \sqrt {50}$
Step 6: $x+8=\pm \sqrt {25\times2}$
Step 7: $x+8=\pm 5\sqrt {2}$
Step 8: $x+8=5\sqrt 2$ or $x+8=-5\sqrt 2$
Step 9: $x=-8+5\sqrt 2$ or $x=-8-5\sqrt 2$
The solution set is {$-8-5\sqrt 2,-8+5\sqrt 2$}.
