# G.6.6.2 Complete the Process

- Author:
- Katie Akesson

Here is the equation of a circle: x² + y² - 6x - 20y + 105 = 0
Elena wants to find the center and radius of the circle. Here is what she’s done so far.
__Step 1__: x² - 6x + y² - 20y = -105
__Step 2__: x² - 6x + 9 + y² - 20y +100 = -105 + 9 + 100
__Step 3__: x² - 6x + 9 + y² - 20y +100 = 4
1. What did Elena do in the first step?
2. Why did Elena add 9 and 100 to the left side of the equation in Step 2?
3. Why did Elena add 9 and 100 to the right side of the equation in Step 2?
4. What should Elena do next?
5. What are the center and radius of this circle?
6. Draw a graph of the circle below.

The goal was to rewrite the equation in the form (x - h)² + (y - k)² = r². Why did Elena want to do this?