To find the radius of the circle, we need to rewrite the equation of the circle in standard form, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is its radius.
To rewrite the given equation in standard form, we need to complete the square for both x and y terms:
x^2 - 12x + y^2 + 6y + 20 = 0
(x^2 - 12x + 36) + (y^2 + 6y + 9) = -20 + 36 + 9 (adding and subtracting appropriate terms to complete the square)
(x - 6)^2 + (y + 3)^2 = 25
Comparing this equation with the standard form, we see that the center of the circle is (6, -3) and the radius is sqrt(25) = 5.
Therefore, the radius of the circle is 5 units.
HOPE THIS HELPS!