Question

Solve for x using the completing the square method for x² - 8x = 7.

A. x = -8 ± √23
B. x = -8 ± √7
C. x = -4 ± √7

Answer 1

To solve the equation x² - 8x = 7 using the completing the square method, follow these steps: move the constant term, take half and square, add to both sides, write as a perfect square, take square root, and isolate x. The solution is x = 4 ± √23.

Step-by-step explanation:

To solve the equation x² - 8x = 7 using the completing the square method, follow these steps:

1. Move the constant term to the right side of the equation: x² - 8x - 7 = 0.
2. Take half of the coefficient of the x term (-8) and square it: (-8/2)² = (-4)² = 16.
3. Add the result from step 2 to both sides of the equation: x² - 8x + 16 = 7 + 16 = 23.
4. Write the left side as a perfect square: (x - 4)² = 23.
5. Take the square root of both sides: x - 4 = ±√23.
6. Add 4 to both sides to isolate x: x = 4 ± √23.

Therefore, x = 4 ± √23.