Answer:
To complete the square for the equation -5x² + 10x = -315, we can follow these steps:
Move the constant term (-315) to the right side of the equation:
-5x² + 10x + 315 = 0
Divide both sides of the equation by the coefficient of the x^2 term (-5) to get a coefficient of -1 for the x^2 term:
x² - 2x - 63 = 0
Add the square of half the coefficient of the x term to both sides of the equation:
x² - 2x + 1 - 1 - 63 = 0 + 1
Simplify the left side of the equation by factoring the quadratic trinomial and combining like terms:
(x - 1)² - 64 = 1
Add 64 to both sides of the equation:
(x - 1)² = 65
So the intermediate step in completing the square for -5x² + 10x = -315 is:
(x - 1)² - 64 = 1
This is the result of adding the square of half the coefficient of the x term (-1) to both sides of the equation and simplifying.