What is the radius for this given equation? (x^2+10x) + (y^2-8y)=59

The answer to your question is r = 10

Step-by-step explanation:

Data

            (x² + 10x   )  +  (y² - 8y   ) = 59

Process

1.- Complete the perfect square trinomials

             (x² + 10x + (5)²) + (y² - 8y + (4)²) = 59 + (5)² + (4)²

2.- Simplify

             (x² + 10x + 25) + (y² - 8y + 16) = 59 + 25 + 16

3.- Factor

             (x + 5)² + (y - 4)² = 100

or             (x + 5)² + (y - 4)² = 10²

4.- Compare the result with the standard form

                 (x - h)² + (y - k)² = r²

then r² = 10²

and  r = 10