Answer
$\{-3,1\}$
Work Step by Step
We are given the equation:
$$\begin{align}4-(x+1)^2=0.\end{align}$$
Graph $y=4-(x+1)^2$. From the graph we find the $x$-intercepts:
$$\begin{align*}
x_1&=-3\\
x_2&=1.
\end{align*}$$
We check the solutions by substituting them in Eq. $(1)$:
$$\begin{align*}
x_1&=-3\\
4-(-3+1)^2&\stackrel{?}{=}0\\
4-4&\stackrel{?}{=}0\\
0&=0\checkmark\\\\
x_2&=1\\
4-(1+1)^2&\stackrel{?}{=}0\\
4-4&\stackrel{?}{=}0\\
0&=0\checkmark\\
\end{align*}$$
Both solutions check the equation, so the solution set is:
$$\{-3,1\}.$$
