5x² + 40x + 5y² = 0

Divide every term by 5

    x² + 8x + y² = 0

Complete the square with the first two terms:

1. Multiply 8 times  getting 4
2. Square 4 getting 16
3. Add 16 to both sides after the term in y

    x² + 8x + 16 + y² = 0 + 16

Factor the first three terms

      (x+4)(x+4) + y² = 16

          (x+4)² + y² = 16     

Since there is no y-term, we complete the square on y²
simply by writing it as (y-0)².  Write 16 as 4²:

      (x+4)² + (y-0)² = 4²

Compare that to the standard form equation for a circle

      (x-h)² + (y-k)² = r²

The center (h,k) = (-4,0).  The radius r=4



Edwin