College Algebra, Chapter 2, 2.2, Section 2.2, Problem 74

Sketch the graph of the equation $4x^2 + 4y^2 + 2x = 0$


$
\begin{equation}
\begin{aligned}

4x^2 + 4y^2 + 2x =& 0
&& \text{Model}
\\
\\
\left(x^2 + \frac{x}{2} + \underline{ } \right) + y^2 =& 0
&& \text{Group terms}
\\
\\
\left( x^2 + \frac{x}{2} + \frac{1}{16} \right) + y^2 =& \frac{1}{16}
&& \text{Complete the square: add } \left( \frac{\displaystyle \frac{1}{2}}{2} \right)^2 = \frac{1}{16}
\\
\\
\left(x + \frac{1}{4} \right)^2 + y^2 =& \frac{1}{16}
&& \text{Perfect Square}
\end{aligned}
\end{equation}
$


Recall that the general equation for the circle with
circle $(h,k)$ and radius $r$ is..

$(x - h)^2 + (y - k)^2 = r^2$

By observation,

The center is at $\displaystyle \left( \frac{-1}{4}, 0 \right)$ and the
radius is $\displaystyle \sqrt{\frac{1}{16}} = \frac{1}{4}$.