Write the equation of the circle x^2+y^2+6x-2y-6=0 in the standard form.

Given: x^2 + y ^2 + 6x - 2y - 6 =
0

1. Group the x's together, group the y's together: x^2 +
6x + y^2 - 2y - 6 = 0.

2. Move the numbers to the other
side of the equation (add 6): x^2 + 6x + y^2 - 2y = 6.

3.
Complete the squares for the 'x' and 'y' terms (halve the coefficient of the x/y term,
then square it. Because we are adding this to the left hand side of the equation, we
must also add it to the right-hand side in order to maintain equality): x^2 + 6x + 9 +
y^2 - 2y + 1= 6 + 9 + 1. --> x^2 + 6x + 9 + y^2 - 2y + 1 =
16.

4. Factor the perfect squares you created in the above
step: (x + 3)^2 + (y - 1)^2 = 16.