Answer
The required solution is $\left\{ -2\pm i\sqrt{2} \right\}$
Work Step by Step
We have to write the general form of a quadratic equation:
$a{{x}^{2}}+bx+c=0$
Write the given equation:
${{x}^{2}}+4x+6=0$
Identify the values of $a$ , $b$ , and $c$.
Thus, $a=1$ , $b=4$ , and $c=6$.
Use the following quadratic formula:
$x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
Put $1$ for $a$, $4$ for $b$, and $6$ for $c$:
$\begin{align}
& x=\frac{-4\pm \sqrt{{{\left( 4 \right)}^{2}}-4\left( 1 \right)\left( 6 \right)}}{2\left( 1 \right)} \\
& =\frac{-4\pm \sqrt{16-24}}{2} \\
& =\frac{-4\pm \sqrt{-8}}{2} \\
& =\frac{-4\pm i2\sqrt{2}}{2}
\end{align}$
Solve further,
$x=-2\pm i\sqrt{2}$
Hence, the solution is $\left\{ -2\pm i\sqrt{2} \right\}$.
