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√(1^2-4(1)(5))}{2(1)}\implies x=\cfrac{-1\pm√(-19)}{2} \\\\\\ x=\cfrac{-1\pm√(-1\cdot 19)}{2}\implies x=\cfrac{-1\pm√(-1)\cdot √(19)}{2} \\\\\\ x=\cfrac{-1\pm i √(19)}{2}`