To complete the square for the expression x² – 18x, we need to find a value that allows us to express it in the form of a perfect square trinomial.
First, we take the coefficient of the linear term, which in this case is -18. We divide this value by 2, giving us -9. Next, we square this result: (-9)² = 81.
Now we can rewrite the expression by adding and subtracting this squared value:
x² – 18x + 81 – 81.
This rearranges to:
(x – 9)² – 81.
Thus, the value that completes the square for the expression x² – 18x is 81.