Question

Solve the quadratic equation by completing the square. (Enter your answers as a comma-separated list. If an answer does not exist, entor ore.) x²−8x−9=0 -10

Answer 1

To solve the given quadratic equation by completing the square, follow these steps: Move the constant term to the right side, complete the square by adding the square of half the coefficient of x to both sides, factor the left side, take the square root of both sides, and solve for x.

Step-by-step explanation:

To solve the quadratic equation x²-8x-9=0 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation: x²-8x=9
2. Complete the square by adding the square of half the coefficient of x to both sides of the equation. The coefficient of x is -8, so half of it is -4. Adding (-4)²=16 to both sides gives us: x²-8x+16=9+16
3. Factor the left side of the equation: (x-4)² = 25
4. Take the square root of both sides: x-4 = ±√(25)
5. Solve for x: x = 4±√(25)

Therefore, the solutions to the quadratic equation x²-8x-9=0 are x = 4+√(25) and x = 4-√(25), which simplify to x = 9 and x = -1, respectively.