Write and graph the equation of a circle: ${\mathit{x}}^{\mathbf{2}}\mathbf{+}{\mathit{y}}^{\mathbf{2}}\mathbf{–}\mathbf{20}\mathit{x}\mathbf{+}\mathbf{10}\mathit{y}\mathbf{=}\mathbf{–}\mathbf{116}$

$$\begin{gathered} \left(x^2–20x+{\left(\boxed{\frac{–20}{2}}\right)}^2\right)+\left(y^2+10y+{\left(\boxed{\frac{10}{2}}\right)}^2\right)=–116+{\left(\boxed{\frac{–20}{2}}\right)}^2+{\left(\boxed{\frac{10}{2}}\right)}^2 \\ {\left(x–10\right)}^2+{\left(y+5\right)}^2=–116+{\left(–10\right)}^2+{\left(5\right)}^2 \\ {\left(x–10\right)}^2+{\left(y+5\right)}^2=–116+100+25 \\ {\left(x–10\right)}^2+{\left(y+5\right)}^2=9 \end{gathered}$$