Solve the quadratic equation by completing the square. \[ x^{2}+2 x=63 \] \( x=\square \) (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use a comma to separate answers as needed.)

To solve the quadratic equation \( x^{2}+2x=63 \) by completing the square, we first rearrange the equation: \[ x^2 + 2x - 63 = 0. \] Next, we'll isolate the quadratic and linear terms: \[ x^2 + 2x = 63. \] Now, to complete the square, take half of the coefficient of \( x \) (which is 2), square it (resulting in 1), and add it to both sides: \[ x^2 + 2x + 1 = 63 + 1, \] \[ (x + 1)^2 = 64. \] Take the square root of both sides: \[ x + 1 = \pm 8. \] Now, solve for \( x \): 1. \( x + 1 = 8 \) leads to \( x = 7 \), 2. \( x + 1 = -8 \) leads to \( x = -9 \). Thus, the solutions to the equation are: \( x = 7, -9 \).