Using the following equation, find the center and radius of the circle. you must show all work and calculations to receive credit.
x^2 + 2x + y^2 + 4y = 20

The center is (-1,-2) and the radius is 5.

Step-by-step explanation:

Our goal is to write in the standard form, the form I like to call center-radius form because it tells you the center and the radius; that equation looks like

where (h,k) is the center and r is the radius.

So this means we need to complete the square. I'm going to use this handy dandy formula to help me to so:

.

Make sure the x's are together and the y's are together and the constant on the opposing side. It already is.

Leave spaces for the thing we need to add to the x part and the y part to complete the square for both.  Remember whatever you add on one side you must add to the other side:

Now the first blank in going to contain (2/2)^2.  I just compared x^2+2x+___ to x^2+bx+(b/2)^2 to figure out what goes in that first blank.

So one of the other blanks on the opposing side will also contain that quantity.

Now the second blank is going to contain (4/2)^2. I just compared y^2+4y+___ to y^2+by+(b/2)^2 to figure out what goes in that second blank.

So one of the other blanks on the opposing side will contain that quantity also.

I'm going to go ahead and write that left hand side now has the sum of two squares one containing the x variable and the other the y. I need to use this:

.

Now I'm ready to do any simplifying:

Compare this to:

-h=1 and -k=2 and r^2=25

h=-1 and k=-2 and r=5

The center is (-1,-2) and the radius is 5.