Solve the following equation by completing the square. \[ x^{2}+2 x=15 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \left\{\begin{array}{l}\text { (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) } \\ \text { B. There is no solution. }\end{array}\right. \)

To solve the equation \( x^{2} + 2x = 15 \) by completing the square, follow these steps: 1. **Move the constant term to the other side:** \[ x^{2} + 2x = 15 \quad \Rightarrow \quad x^{2} + 2x - 15 = 0 \] 2. **Complete the square:** - Take the coefficient of \( x \), which is 2, divide it by 2 to get 1, and then square it to get 1. - Add and subtract this square inside the equation: \[ x^{2} + 2x + 1 = 15 + 1 \quad \Rightarrow \quad (x + 1)^2 = 16 \] 3. **Take the square root of both sides:** \[ x + 1 = \pm 4 \] 4. **Solve for \( x \):** \[ x = -1 \pm 4 \] - \( x = -1 + 4 = 3 \) - \( x = -1 - 4 = -5 \) **Solution Set:** \[ \{3, -5\} \] **Answer:** **A.** The solution set is \( \{3, -5\} \).