The equation x^{2} + y^{2} + 6x – 4y – 3 = 0, for example, is the equation of a circle. You can change this equation to the standard form by completing the square for each of the variables. Just follow these steps:

Change the order of the terms so that the x's and y's are grouped together and the constant appears on the other side of the equal sign.
Leave a space after the groupings for the numbers that you need to add:
x^{2} + 6x _____ + y^{2} – 4y _____ = 3

Complete the square for each variable, adding the number that creates perfect square trinomials.
In the case of the x's, you add 9, and with the y's, you add 4. Don't forget to also add 9 and 4 to the right:
x^{2} + 6x + 9 + y^{2} – 4y + 4 = 3 + 9 + 4
When it's simplified, you have x^{2} + 6x + 9 + y^{2} – 4y + 4 = 16

Factor each perfect square trinomial.
The standard form for the equation of this circle is (x + 3)^{2} + (y – 2)^{2} = 16.