Final answer:
To solve x² + 2x - 48 = 0 by completing the square, add (b/2)² to both sides to form a perfect square trinomial. Taking the square root of both sides yields x + 1 = ±√49 and solving for x gives the two solutions, x = 6 and x = -8.
Step-by-step explanation:
To solve the quadratic equation x² + 2x - 48 = 0 by completing the square, follow these steps:
- Move the constant term to the right side of the equation: x² + 2x = 48.
- Find a number that completes the square for the expression on the left to make it a perfect square trinomial. The number you need to add to both sides of the equation is (b/2)², where b is the coefficient of x, which is 2 in this case. So, (2/2)² = 1² = 1. The equation becomes x² + 2x + 1 = 48 + 1.
- Now the left side is a perfect square, (x + 1)² = 49.
- Take the square root of both sides to get x + 1 = ±√49.
- Solve for x by subtracting 1 from both sides: x = -1 ± 7.
- So the two solutions are x = 6 and x = -8.