Answer
{$\frac{-3- 4\sqrt {2}}{5},\frac{-3+4\sqrt {2}}{5}$}
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: $(5x+3)^{2}=32$
Step 2: $5x+3=\pm \sqrt {32}$
Step 3: $5x+3=\pm \sqrt {16\times2}$
Step 4: $5x+3=\pm \sqrt {4^{2}\times2}$
Step 5: $5x+3=\pm 4\sqrt {2}$
Step 6: $5x+3=+ 4\sqrt {2}$ or $5x+3=-4 \sqrt {2}$
Step 7: $5x=-3+ 4\sqrt {2}$ or $5x=-3-4 \sqrt {2}$
Step 8: $x=\frac{-3+ 4\sqrt {2}}{5}$ or $x=\frac{-3- 4\sqrt {2}}{5}$
The solution set is {$\frac{-3- 4\sqrt {2}}{5},\frac{-3+4\sqrt {2}}{5}$}.
