1. **State the problem:** Find the center and radius of the circle given by the equation $$x^2 + y^2 + 2x - 6y + 5 = 0$$. 2. **Rewrite the equation:** Group $x$ and $y$ terms: $$x^2 + 2x + y^2 - 6y = -5$$ 3. **Complete the square:** For $x$ terms: $$x^2 + 2x = (x+1)^2 - 1^2 = (x+1)^2 - 1$$ For $y$ terms: $$y^2 - 6y = (y-3)^2 - 3^2 = (y-3)^2 - 9$$ 4. **Substitute back:** $$(x+1)^2 - 1 + (y-3)^2 - 9 = -5$$ 5. **Simplify:** $$(x+1)^2 + (y-3)^2 - 10 = -5$$ $$(x+1)^2 + (y-3)^2 = 5$$ 6. **Identify center and radius:** Center: $$(-1, 3)$$ Radius: $$\sqrt{5}$$ **Final answer:** The circle has center at $(-1,3)$ and radius $\sqrt{5}$.