Answer
$y=-\dfrac{1}{2}$
Work Step by Step
The factored form of the given expression, $
y^2+\dfrac{1}{4}=-y
$, is
\begin{array}{l}
y^2+y+\dfrac{1}{4}=0
\\\\
\left( y+\dfrac{1}{2} \right)\left( y+\dfrac{1}{2} \right)=0
\\\\
\left( y+\dfrac{1}{2} \right)\left( y+\dfrac{1}{2} \right)=0
\\\\
\left( y+\dfrac{1}{2} \right)^2=0
.\end{array}
Using the Square Root Property, then
\begin{array}{l}
y+\dfrac{1}{2}=\pm\sqrt{0}
\\\\
y+\dfrac{1}{2}=0
\\\\
y=0-\dfrac{1}{2}
\\\\
y=-\dfrac{1}{2}
\end{array}
