Final answer:
To complete the square for the equation y = x^2 - 18x, you need to add 81 to both sides of the equation.
Step-by-step explanation:
To complete the square for the equation y = x^2 - 18x, we need to find the value that when added to both sides of the equation, will make the left side a perfect square trinomial.
The value we need to add is half of the coefficient of the x term, squared. In this case, the coefficient of the x term is -18, so we add (18/2)^2 = 9^2 = 81 to both sides.
Adding 81 to both sides gives us y + 81 = x^2 - 18x + 81. Now, we can rewrite the right side as a perfect square: y + 81 = (x - 9)^2.
So, in order to complete the square for the equation y = x^2 - 18x, we add 81 to both sides of the equation.