Answer
multiple answers; see details
Work Step by Step
The standard form of the equation $
x^2+y^2+2x+y=\dfrac{3}{4}
$ is
\begin{array}{l}
(x^2+2x)+(y^2+y)=\dfrac{3}{4}\\\\
(x^2+2x+1)+\left(y^2+y+\dfrac{1}{4}\right)=\dfrac{3}{4}+1+\dfrac{1}{4}\\\\
(x+1)^2+\left(y+\dfrac{1}{2}\right)^2=2
.\end{array}
The graph of this equation is a $\text{
circle
}$ with the following properties:
\begin{array}{l}
\text{Center: }\left(
-1,-\dfrac{1}{2}
\right),\\\\\text{Radius: }
\sqrt{2}
.\end{array}
Using the properties above, the graph of the equation is given below.
