Question 16112
You want to get your equation into the standard form for a circle with center at (h, k) and radius r.  It will look like this:
{{{(x - h)^2 + (y - k)^2 = r^2}}}

To do this, you must:

1) Complete the square in the x-terms.
2) Complete the square in the y-terms.
3) Factor the resulting x-trinomial.
4) Factor the resulting y-trinomial.
5) Simplify, if necessary, into the standard form.

{{{(x^2 + 6x) + (y^2 - 5y) = -1/4}}} Complete the squares by adding the square of half the coefficient of x/y to both sides.
{{{(x^2 + 6x + 9) + (y^2 - 5y + 25/4) = -1/4 + 9 + 25/4}}} Factor the x and the y trinomials and simplify the right side of the equation.
{{{(x + 3)^2 + (y - 5/2)^2 = 15}}} Compare this with the standard form. {{{(x-h)^2 + (y-k)^2 = r^2}}}

The center of the circle is at (-3, 5/2) and the radius is {{{sqrt(15)}}}