Solve the following equation by completing the square. \( x^{2}+2 x-9=0 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are \( x=\square \) (Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.) B. No real solutions.

To solve the equation \( x^{2}+2x-9=0 \) by completing the square, we start by moving the constant term to the other side: \[ x^2 + 2x = 9. \] Next, we take half of the coefficient of \( x \) (which is 2), square it, and add it to both sides: \[ \left(\frac{2}{2}\right)^2 = 1. \] So, we add 1 to both sides: \[ x^2 + 2x + 1 = 10. \] Now, we can rewrite the left side as a perfect square: \[ (x + 1)^2 = 10. \] Taking the square root of both sides gives us: \[ x + 1 = \pm \sqrt{10}. \] Finally, solving for \( x \) gives: \[ x = -1 \pm \sqrt{10}. \] Thus, the solutions are: A. The solution(s) is/are \( x = -1 + \sqrt{10}, -1 - \sqrt{10} \).