Question

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

A. {-7, 1}
B. 1-3 - 10. - 3+ 10)
C. 13 - 10,3 + 10)
D. {1,7)

Answer 1

To solve x² + 6x = 7 by completing the square, move the constant term to the right side and add the square of half of the coefficient of x to both sides. The solution set is {-7, 1}.

Step-by-step explanation:

To solve the equation x² + 6x = 7 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation: x² + 6x - 7 = 0
2. Take half of the coefficient of x, square it, and add it to both sides of the equation: x² + 6x + (6/2)² = 7 + (6/2)²
3. Simplify: x² + 6x + 9 = 7 + 9
4. Factor the perfect square trinomial: (x + 3)² = 16
5. Take the square root of both sides: x + 3 = ± √16
6. Solve for x: x = -3 ± 4

The solution set of the equation x² + 6x = 7 is {-7, 1}. Therefore, the correct answer is option A. {-7, 1}