\(\Leftrightarrow\left(x^2+2x+1\right)+\left(y^2-y+\frac{1}{4}\right)=0\)
\(\Leftrightarrow\left(x+1\right)^2+\left(y-\frac{1}{2}\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+1=0\\y-\frac{1}{2}=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=-1\\y=\frac{1}{2}\end{matrix}\right.\)