To complete the square for the given equation, we need to first move all the constant terms to one side and all the variable terms to the other side. This can be done as follows:
x² + 40x + 45 = 0
Next, we need to take half of the coefficient of x (which is 40) and square it, i.e., (40/2)² = 400. We then add and subtract this value on both sides of the equation as follows:
x² + 40x + 400 - 400 + 45 = 0
Now, we can write the first three terms on the left-hand side as a perfect square, i.e., (x + 20)². Simplifying the rest of the equation, we get:
(x + 20)² = -5
Therefore, the intermediate step in completing the square for the given equation is:
x² + 40x + 400 - 400 + 45 = 0
(x + 20)² - 355 = 0
(x + 20)² = 355