Using the following equation, find the center and radius of the circle:
x2 + y2 +2x − 4y − 20 = 0. show all work.

Comlete the square sepereately for x's and y's
get into the form
(x-h)^2+(y-k)^2=r^2
(h,k) is vertex and r is radius
so

gropu x and y's togethter
(x^2+2x)+(y^2-4y)-20=0
since the coefients of the squared terms are 1, this makes it easier
take 1/2 of each linear coefient and square it, then add those to both sides
2/2=1, 1^2=1

-4/2=-2, (-2)^2=4
add 1+4 to both sides
(x^2+2x+1)+(y^2-4y+4)-20=4+1
factor perfect squares
(x+1)^2+(y-2)^2-20=5
add 20 to both sides
(x+1)^2+(y-2)^2=25
(x-(-1))^2+(y-2)^2=5^2
center is (-1,2) and radius is 5

X2 + 2x + y2 - 4y = 20
x2 + 2x + 1 + y2  - 4y + 4 = 20 + 1 + 4
(x+1)2 + (y-2)2 = 25
therefore r= 5
c (-1, 2)