\( x^{2}+12 x+45=0 \). Enter multiple answers as a list separated by commas. Example: \( 2+2 i, 2-2 i \)

Solve the equation \( x^{2}+12x+45=0 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(x^{2}+12x+45=0\) - step1: Solve using the quadratic formula: \(x=\frac{-12\pm \sqrt{12^{2}-4\times 45}}{2}\) - step2: Simplify the expression: \(x=\frac{-12\pm \sqrt{-36}}{2}\) - step3: Simplify the expression: \(x=\frac{-12\pm 6i}{2}\) - step4: Separate into possible cases: \(\begin{align}&x=\frac{-12+6i}{2}\\&x=\frac{-12-6i}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&x=-6+3i\\&x=\frac{-12-6i}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=-6+3i\\&x=-6-3i\end{align}\) - step7: Rewrite: \(x_{1}=-6-3i,x_{2}=-6+3i\) - step8: Remove the complex number(s): \(\textrm{No real solution}\) The equation \(x^{2}+12x+45=0\) does not have any real solutions. Therefore, the solutions are complex numbers. Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(x^{2}+12x+45=0\) - step1: Solve using the quadratic formula: \(x=\frac{-12\pm \sqrt{12^{2}-4\times 45}}{2}\) - step2: Simplify the expression: \(x=\frac{-12\pm \sqrt{-36}}{2}\) - step3: Simplify the expression: \(x=\frac{-12\pm 6i}{2}\) - step4: Separate into possible cases: \(\begin{align}&x=\frac{-12+6i}{2}\\&x=\frac{-12-6i}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&x=-6+3i\\&x=\frac{-12-6i}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=-6+3i\\&x=-6-3i\end{align}\) - step7: Rewrite: \(x_{1}=-6-3i,x_{2}=-6+3i\) The solutions to the equation \(x^{2}+12x+45=0\) are \(x=-6-3i\) and \(x=-6+3i\).