Answer
{$\frac{-3- 2\sqrt {5}}{2},\frac{-3+ 2\sqrt {5}}{2}$}
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: $(2n+3)^{2}=20$
Step 2: $2n+3=\pm \sqrt {20}$
Step 3: $2n+3=\pm \sqrt {4\times5}$
Step 4: $2n+3=\pm \sqrt {2^{2}\times5}$
Step 5: $2n+3=\pm 2\sqrt {5}$
Step 6: $2n+3=+ 2\sqrt {5}$ or $2n+3=-2 \sqrt {5}$
Step 7: $2n=-3+ 2\sqrt {5}$ or $2n=-3-2 \sqrt {5}$
Step 8: $n=\frac{-3+ 2\sqrt {5}}{2}$ or $n=\frac{-3- 2\sqrt {5}}{2}$
The solution set is {$\frac{-3- 2\sqrt {5}}{2},\frac{-3+ 2\sqrt {5}}{2}$}.
