Question

Solve x^2 + X + 5= 0 using the quadratic formula. what is the solution set?

Answer 1

$\bf ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \begin{array}{llcccl} & 1 x^2& +1 x& +5&=0\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-1\pm\sqrt{1^2-4(1)(5)}}{2(1)}\implies x=\cfrac{-1\pm\sqrt{-19}}{2} \\\\\\ x=\cfrac{-1\pm\sqrt{-1\cdot 19}}{2}\implies x=\cfrac{-1\pm\sqrt{-1}\cdot \sqrt{19}}{2} \\\\\\ x=\cfrac{-1\pm i \sqrt{19}}{2}$