Answer:
the solutions to the quadratic equation x² + 16x - 17 = 0 using the completing the square method are x = 1 and x = -17.
Explanation:
1. Move the constant term to the other side of the equation:
x² + 16x = 17
2. To complete the square, take half of the coefficient of x (which is 16) and square it. Add this result to both sides of the equation:
x² + 16x + 64 = 17 + 64
x² + 16x + 64 = 81
3. Rewrite the left side of the equation as a perfect square trinomial:
(x + 8)² = 81
4. Take the square root of both sides of the equation:
x + 8 = ±√81
x + 8 = ±9
5. Solve for x by subtracting 8 from both sides of the equation:
x = -8 ± 9
6. Simplify the solutions:
x = 1 or x = -17