Answer:
x = 15 and x = 10
Explanation:
To complete the square for the quadratic equation -10x² + 250x - 1500 = 0, follow these steps:
1. Divide the entire equation by the coefficient of x² to make the coefficient of x² equal to 1:
-10x² + 250x - 1500 = 0
Dividing by -10, we get:
x² - 25x + 150 = 0
2. Move the constant term (in this case, 150) to the right-hand side of the equation:
x² - 25x = -150
3. Add the square of half of the coefficient of x to both sides of the equation:
x² - 25x + (25/2)² = -150 + (25/2)²
Note that (25/2)² = 625/4.
x² - 25x + 625/4 = -150 + 625/4
4. Simplify the right-hand side of the equation:
x² - 25x + 625/4 = 25/4
5. Factor the left-hand side of the equation as a perfect square trinomial:
(x - 25/2)² = 25/4
6. Take the square root of both sides of the equation:
x - 25/2 = ±5/2
7. Solve for x:
x = (25 ± 5)/2
x = 15 or x = 10
Therefore, the solutions to the equation -10x² + 250x - 1500 = 0 are x = 15 and x = 10.