Final answer:
The diameter of the circle given by the equation x² + y² + 10x - 4y = 20 is approximately 13.42 units.
Step-by-step explanation:
To find the diameter of the circle given by the equation x² + y² + 10x - 4y = 20, we first need to rearrange the equation to the standard form of a circle equation, which is (x - h)² + (y - k)² = r². In this case, the equation can be rewritten as (x + 5)² + (y - 2)² = 45. Comparing this with the standard form, we can see that the center of the circle is (-5, 2) and the radius squared is 45. So, the radius is the square root of 45, which is approximately 6.71 units. Therefore, the diameter of the circle is twice the radius, which is approximately 13.42 units.