\(\left(x-\frac{1}{2}\right)^2=16\)

\(\left(x-\frac{1}{2}\right)^2=4^2\)

\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{2}=4\\x-\frac{1}{2}=-4\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=\frac{9}{2}\\x=-\frac{7}{2}\end{cases}}\)