Solve this equation and select the choice that contains all of the solutions. \[ x^{2}+2 x+10=0 \]

To solve the equation \( x^{2}+2x+10=0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = 2 \), and \( c = 10 \). First, calculate the discriminant: \[ b^2 - 4ac = 2^2 - 4(1)(10) = 4 - 40 = -36 \] Since the discriminant is negative, there are no real solutions. Instead, we have complex solutions: \[ x = \frac{-2 \pm \sqrt{-36}}{2(1)} = \frac{-2 \pm 6i}{2} = -1 \pm 3i \] Thus, the solutions are \( x = -1 + 3i \) and \( x = -1 - 3i \).