Complete the square to rewrite the following equation. identify the center and radius of the circle. x2+2x+y2+4y=20

Q: x^2+2x+y2+4y=20

A:

Step A1. Complete square for X^2+2x
Step A2. Divide your "b" term in half and then square it.
... So half of 2 from 2x is 1. And 1^2 is 1.
Step A3. Complete this square which is (x+1)^2
Step A4. Add the remaining squared term "b" and add it to 20.

Next...
Step B1. Complete square for y^2+4y
Step B2. Apply step A2. here
Step B3. (y+2)^2
Step B4. Similar to step A4.

Sooo...

Q: X^2+2x+y^2+4y=20
A : (x+1)^2 + (y+2)^2 = 20+1+4
Recall formula: (x+h)^2 + (y+k)^2 = r^2

So... (x+1)^2 + (y+2)^2 = 25 <<And that means (x+2)^2 + (y+2)^2 = 5

Your radius is 5 and your center is (-1, -2)