Answer
$-13+\sqrt{199}$; $-13-\sqrt{199}$
Work Step by Step
Given \begin{equation}
x^2+26 x=30.
\end{equation} Apply the method of completing the square to solve for $x$. Make sure that the coefficient of the square term is one before adding half the square of the coefficient of the $x$ term to both sides. \begin{equation}
\begin{aligned}
x^2+26 x& =30\\
x^2+2\cdot 13x+13^2 & =30+13^2 \\
(x+13)^2 & =199 \\
x+13 & = \pm \sqrt{199} \\
x & =-13 \pm \sqrt{199}.
\end{aligned}
\end{equation} This gives: \begin{equation}
\begin{aligned}
& x=-13+\sqrt{199} \\
& \approx 1.1067 \\
& x=-13-\sqrt{199} \\
& \approx-27.1067
\end{aligned}
\end{equation} Check: \begin{equation}
\begin{aligned}
(-13+\sqrt{199})^2+26(-13+\sqrt{199}) & \stackrel{?}{=}30 \\
169-26\sqrt{199}+199-338+26\sqrt{199}& \stackrel{?}{=} 30\\
30 & =30\checkmark\\\\
(-13-\sqrt{199})^2+26(-13-\sqrt{199}) & \stackrel{?}{=}30 \\
169+26\sqrt{199}+199-338-26\sqrt{199}& \stackrel{?}{=} 30\\
30 & =30\checkmark.
\end{aligned}
\end{equation} The solution is $$x=-13+\sqrt{199},\quad x=-13-\sqrt{199}.$$
