Answer:
The answer to your question is 2√233 ≈ 30.5
Step-by-step explanation:
Data
(x² + 24x ) + (y² + 4y ) = 85
Process
1.- Complete the perfect square trinomials
(x² + 24x + (12)²) + (y² + 4y + (2)²) = 85 + 12² + 2²
2.- Simplify
(x² + 24x + 144) + (y² + 4y + 4) = 85 + 144 + 4
(x + 12)² + (y + 2)² = 233
3.- Calculate the radius
radius² = 233
radius = √233
diameter = 2radius
diameter = 2√233 ≈ 30.5
