Find the radius of the circle with equation x^2 - 4x + y^2 - 6y - 36 = 8x - 20y.
+2666 Simplify the equation to: \(x^2-12x+y^2+14y=36\)
Complete the square for the left hand side:\((x-6)^2+(y-7)^2\)
Simplifying this gives us: \(x^2-12+y^2+14y+85\)
Since we added 85 to the left hand side, we have to add 85 to the right hand side as well.
This gives us: \((x-6)^2+(y+7)^2=121\)
The right-hand side is the radius squared, so we have the equation: \(121 = r^2\)
Solving, we find \(\color{brown}\boxed{r = 11} \)
