Final answer:
To complete the square for the equation x² - 18x + 9 = 17, you would add 81 to both sides, which is the square of half the coefficient of x (half of -18 is -9; -9 squared is 81).
Step-by-step explanation:
In order to complete the square for the equation x² - 18x + 9 = 17, we want to form a perfect square trinomial on the left side. This involves adding the square of half the coefficient of x to both sides. So, we take the coefficient of x, which is -18, divide it by 2 to get -9, and then square it to get 81. We will add 81 to both sides of the equation.
The equation with the complete square will look like this: x² - 18x + 81 = 17 + 81. After addition, the equation simplifies to (x - 9)² = 98. So the number you would need to add to both sides of the equation is 81.