Answer
$x =-\frac{5}{4} +\frac{\sqrt{39}}{4}\ i$
$x=-\frac{5}{4}-\frac{\sqrt{39}}{4}\ i$
Work Step by Step
Given the quadratic equation
\begin{equation}
2 x^2+5 x+4=-4.
\end{equation} This equation can be best solved by the quadratic formula.after rewriting it in the form
\begin{equation}
\begin{aligned}
ax^2+bx+c&=0\\
2 x^2+5 x+4&=-4 \\
2 x^2+5 x+8&=0\\
\end{aligned}
\end{equation} Identify $a$, $b$, $c$ and determine the solutions:\begin{equation}
\begin{aligned}
a & =2, b=5, c=8 \\
x & =\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\
x & =\frac{-5 \pm \sqrt{5^2-4 \cdot 2(8)}}{2 \cdot 2}\\
& =\frac{-5\pm \sqrt{-39}}{4} \\
&=\frac{-5\pm \sqrt{39}}{4}\ i.
\end{aligned}
\end{equation} The solution is
\begin{equation}
\begin{aligned}
x& =-\frac{5}{4} +\frac{\sqrt{39}}{4}\ i\\
x& =-\frac{5}{4}-\frac{\sqrt{39}}{4}\ i.
\end{aligned}
\end{equation}
