Question

Solve x^2 + 10x = 24 by completing the square. What is the solution set of the equation?

A) -5 - √34, -5 + √34
B) -5 - √29, -5 + √29
C) -12, 2
D) -2, 12

Answer 1

To solve the equation x^2 + 10x = 24 by completing the square, we manipulate the equation to form a perfect square trinomial, take the square root of both sides and then solve for x, resulting in a solution set of {-12, 2}.

Step-by-step explanation:

We're tasked with solving the quadratic equation x^2 + 10x = 24 by completing the square. To do this, we'll move the constant term to the other side and find the number that makes the left-hand side a perfect square trinomial.

1. Firstly, subtract 24 from both sides to get x^2 + 10x - 24 = 0.
2. Add 25 to both sides, which is the square of half the x-coefficient, to get x^2 + 10x + 25 = 49.
3. Now we have a perfect square on the left: (x + 5)^2 = 49.
4. Take the square root of both sides to get x + 5 = ±√49.
5. Subtract 5 from both sides to obtain the solution set x = -5 ± √49.
6. Since √49 is 7, the solutions are x = -5 - 7 and x = -5 + 7.
7. Therefore, the solution set is {-12, 2}.

By completing the square, we find that the solution set is C) -12, 2.