Answer
{$-\frac{1}{2},-1$}
Work Step by Step
Using Property 10.1, which states that for any non-negative real number $a$, $(x+b)^{2}=a$ can be written as $x+b=\pm\sqrt a$, we obtain:
Step 1: $(4x+3)^{2}=1$
Step 2: $4x+3=\pm \sqrt {1}$
Step 3: $4x+3=\pm 1$
Step 4: $4x+3=1$ or $4x+3=-1$
Step 5: $4x=1-3$ or $4x=-1-3$
Step 6: $4x=-2$ or $4x=-4$
Step 7: $x=-\frac{1}{2}$ or $x=-\frac{4}{4}=-1$
The solution set is {$-\frac{1}{2},-1$}.
