What is the radius of the circle x 2 + y 2 = - 8 – 9x ? Write your answer in simplified, rationalized form

x^2 + y^2 = - 8 – 9x    move the -9x term to the left side  [it changes signs]

x^2 + 9x + y^2   = -8        complete the square on x

x^2 + 9x + 81/4 + y^2  = -8 + 81/4      simplify

(x + 9/2) + y^2   =  -32/4 + 81/4

(x + 9/2)^2  + y^2  = 49/4

The right side is the radius squared......so......take the square root to find the radius  = sqrt(49/4)  = 7/2  = 3.5  units

Here's a graph of the original function :  https://www.desmos.com/calculator/2s9iegula0