We can factor out the common factor of 9 to get \[ 9x^2 + 9. \] To make this a perfect square trinomial, we need to add and subtract the square of half of the coefficient of the x-term (which is 0.5 times 0.9 = 0.45). So, we have \[ 9x^2 + 9 + (0.45)^2 - (0.45)^2 = (3x + 0.45)^2 - 0.2025. \] Therefore, the answer is \[ 9 x^{2} + 9x + 9 = \boxed{(3x + 0.45)^2 - 0.2025}. \]