Solve the equation.
-$$x ^ { 2 } + x + 5 = 0$$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $x^2 + x + 5 = 0$, we use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = 1$, and $c = 5$. Plugging these values in, we get $x = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1} = \frac{-1 \pm \sqrt{1 - 20}}{2} = \frac{-1 \pm \sqrt{-19}}{2}$. Since $\sqrt{-19}$ is imaginary, we rewrite it as $\sqrt{19}i$, giving $x = -\frac{1}{2} \pm \frac{\sqrt{19}}{2}i$, which matches option D.

Solve the Equation x2+x+5=0x ^ { 2 } + x + 5 = 0x2+x+5=0

Solve the Equation $x ^ { 2 } + x + 5 = 0$