Solve \(x^2-6x+14=0\)  by completing the square

\begin{align}x^2-6x+14 & =0 \\ (x-3)^2-9 +14 & = 0\\ (x-3)^2 & = -5\\ x-3 & = \pm \sqrt{-5}\\ x & = 3 \pm \sqrt{5 \; \times -1}\\ x & = 3 \pm i\sqrt{5} \end{align}

Solve \(x^2-6x+14=0\)  using the quadratic formula

\begin{align}x & = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ & =\frac{6 \pm \sqrt{(-6)^2-4(1)(14)}}{2(1)} \\ & =\frac{6 \pm \sqrt{-20}}{2}\\ & =\frac{6 \pm \sqrt{4 \; \times \; 5 \times -1}}{2}\\ & =\frac{6 \pm 2i \sqrt{5}}{2}\\ & = 3 \pm i \sqrt{5} \end{align}