Answer
{$- \frac{5\sqrt 2}{4}, \frac{5\sqrt 2}{4}$}
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: $8n^{2}=25$
Step 2: $n^{2}=\frac{25}{8}$
Step 3: $x=\pm \sqrt {\frac{25}{8}}$
Step 4: $x=\pm \frac{\sqrt {25}}{\sqrt 8}$
Step 5: $x=\pm \frac{\sqrt {25}}{\sqrt {4\times2}}$
Step 6: $x=\pm \frac{5}{2\sqrt 2}$
Step 7: $x=\pm \frac{5}{2\sqrt 2}\times\frac{2\sqrt 2}{2\sqrt 2}$
Step 8: $x=\pm \frac{10\sqrt 2}{(2\sqrt 2)^{2}}$
Step 9: $x=\pm \frac{10\sqrt 2}{4 \times 2}$
Step 10: $x=\pm \frac{5\sqrt 2}{4}$
The solution set is {$- \frac{5\sqrt 2}{4}, \frac{5\sqrt 2}{4}$}.
