Final answer:
The inequality -x² + 18x - 81 ≤ 0 is true for any value of x because the quadratic expression is a perfect square that has been negated, resulting in a non-positive value which is always less than or equal to zero.
Step-by-step explanation:
To complete the inequality -x² + 18x - 81 ≤ 0 so that it is true for any value of x, we need to determine if the quadratic expression can be factored into a perfect square. By examining the quadratic expression, we can see that it is a transformed version of the perfect square (x-9)² since (-x² + 18x - 81) = -(x² - 18x + 81) = -(x-9)². As the square of a real number is always non-negative, -(x-9)² will be non-positive, and therefore it will always be less than or equal to zero. Thus, the given quadratic expression is indeed always less than or equal to zero, making the inequality -x² + 18x - 81 ≤ 0 true for any value of x.