Question

How do you solve using the quadratic formula for $x^2+x+5=0$?

Answer 1

Solve using the quadratic formula:

The given equation is $x^2+x+5=0$.

From the given quadratic equation consider $a=1$, $b=1$ and $c=5$. Then,

The quadratic formula for the equation $a{x}^2+bx+c=0$ is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

Substitute the values of $a,b$ and $c$ in the quadratic formula to get the solution of the given quadratic equation.

$$\begin{gathered} x=\frac{-1\pm \sqrt{1-4\left(1\right)\left(5\right)}}{2\left(1\right)} \\ \Rightarrow x=\frac{-1\pm \sqrt{1-20}}{2} \\ \Rightarrow x=\frac{-1\pm \sqrt{-19}}{2} \\ \Rightarrow x=\frac{-1\pm \sqrt{-1}\sqrt{19}}{2}(Use\sqrt{-1}=i) \\ \therefore x=\frac{-1\pm i\sqrt{19}}{2} \end{gathered}$$

Hence, the solution of the quadratic equation $x^2+x+5=0$ is $x=\frac{-1\pm i\sqrt{19}}{2}$.