Answer
$t= -3.4 +2\sqrt{ 6} \ i $
$t=-3.4-2\sqrt{ 6} \ i$
Work Step by Step
Given the quadratic equation
\begin{equation}
-0.25(t+3.4)^2+9=15.
\end{equation} This equation can be best solved by completing the square.
\begin{equation}
\begin{aligned}
-0.25(t+3.4)^2+9&=15\\
(t+3.4)^2&=\frac{15-9}{-0.25}\\
(t+3.4)^2&=-24\\
t+3.4&= \pm\sqrt{-4\cdot 6} \\
t& =-3.4 \pm2\sqrt{ 6} \ i.
\end{aligned}
\end{equation} The solution is
\begin{equation}
\begin{aligned}
t & = -3.4 +2\sqrt{ 6} \ i \\
t & =-3.4-2\sqrt{ 6} \ i.
\end{aligned}
\end{equation}
