First, add #color(red)(17)# to each side of the equation to isolate the #r# term while keeping the equation balanced:
#8r^2 - 17 + color(red)(17) = 2471 + color(red)(17)#
#8r^2 - 0 = 2488#
#8r^2 = 2488#
Next, divide each side of the equation by #color(red)(8)# to isolate #r^2# while keeping the equation balanced:
#(8r^2)/color(red)(8) = 2488/color(red)(8)#
#(color(red)(cancel(color(black)(8)))r^2)/cancel(color(red)(8)) = 311#
#r^2 = 311#
Now, take the square root of each side of the equation to solve for #r# while keeping the equation balanced. Remember, the square root of a number produces both a negative and positive result.
#sqrt(r^2) = +-sqrt(311)#
#r = +-sqrt(311) = 17.635# rounded to the nearest thousandth.
