Question Use the square roots property to solve the quadratic equation \( (x+1)^{2}+27=9 \). If there are multiple answers, list them separated by a comma, e.g. 1,2 . If there is no solution, enter \( \varnothing \).

To solve the equation \( (x+1)^{2}+27=9 \), first, we isolate the square term: \[ (x+1)^{2} = 9 - 27 \] \[ (x+1)^{2} = -18 \] Since we have a negative value on the right side, the square root of a negative number indicates that the solutions will involve imaginary numbers. We can express this as: \[ x + 1 = \pm \sqrt{-18} \] This simplifies to: \[ x + 1 = \pm \sqrt{18}i \] \[ x + 1 = \pm 3\sqrt{2}i \] Now, we solve for \( x \): \[ x = -1 \pm 3\sqrt{2}i \] Thus, the solutions to the equation are: \[ \boxed{-1 + 3\sqrt{2}i, -1 - 3\sqrt{2}i} \]