Example 25. Solve the equation

$$
\sqrt{4-6 x-x^{2}}=x+4
$$
Solution. The given equation is equivalent to the system

$$
\left\{\begin{array}{l}
x+4 \geqslant 0 \\
4-6 x-x^{2}=(x+4)^{2}
\end{array}\right.
$$

i.e., the system

$$
\left\{\begin{array}{l}
x \geqslant-4 \\
x^{2}+7 x+6=0
\end{array}\right.
$$

## 68

Solving the equation \(x^{2}+7 x+6=0\), we find its two roots: \(x_{1}=-1\) and \(x_{2}=-6\). The condition \(x \geqslant-4\) is satisfied only by \(x_{1}=-1\). Therefore, the only root of the original equation is the number \((-1)\).