If c is a constant such that 9x^2 + 8x + c is equal to the square of a binomial, then what is c?

9x^2 +8x+c       divide thru by 9  ( x^2 coeff needs to be '1' to 'complete the square')

x^2 + 8/9x                      now take  1/2 of 8/9   (which is 8/18)

(x+8/18)² 

 

x^2 + 16/18  + 64/324   multiply by 9

9x² +  8x     +  16/9