Final Answer:
To solve the quadratic equation x² + 14x = -24 by completing the square. The solution set of the equation x² + 14x = -24 is x = -2 and x = -12. The correct answer is A) (-12, -2).
Step-by-step explanation:
To solve the quadratic equation x² + 14x = -24 by completing the square, follow these steps:
1. Move the constant term to the other side of the equation:
x² + 14x + 24 = 0
2. To complete the square, add and subtract (14/2)² = 49 inside the parenthesis:
x² + 14x + 49 - 49 + 24 = 0
3. Factor the perfect square trinomial:
(x + 7)² - 25 = 0
4. Move the constant term to the other side of the equation:
(x + 7)² = 25
5. Take the square root of both sides:
x + 7 = ± 5
6. Solve for x:
x = -7 ± 5
Now, find the solutions:
x₁ = -7 + 5 = -2
x₂ = -7 - 5 = -12
So, the solution set of the equation x² + 14x = -24 is x = -2 and x = -12.
The correct answer is:
A) (-12, -2)