SOLUTION

The standard form of the equation of a circle is:

(x-h)² + (y-k)² = r²

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

Let’s complete the square for both x and y terms:

x² + 4x + y² + 2y + 4 = 0
(x² + 4x + 4) + (y² + 2y + 1- 1) = 0
(x + 2)² + (y + 1)² = 1

Now we can see that the equation is in the standard form with h = -2, k = -1, and r² = 1.

Therefore, the radius of the circle is the square root of r² which is 1.