Final answer:
The inequality -x² - 4x - 4 ≤ 0 holds true for any value of x because the quadratic expression on the left will always be negative and therefore less than or equal to zero. No further steps are necessary to complete the inequality.
Step-by-step explanation:
To complete the inequality -x² - 4x - 4 ≤ 0 so that it will be true for any value of x, we recognize that the left side of the inequality is always negative because the leading term is -x² and there's no value of x that can make it positive. Therefore, the inequality is always true as it stands because a negative is always less than or equal to zero.
If we were to proceed with trying to solve the inequality, we would look for the roots using the quadratic formula. The quadratic formula is used for equations of the form ax² + bx + c = 0 and gives the solutions for x. However, because the quadratic coefficient is negative and this is a downward-opening parabola, it will not intersect the x-axis, meaning the inequality is true for all x.