Answer
$x=-3$ and $x=3$
Work Step by Step
We solve the given equation:
$$\begin{align*}
(x+1)^2&=2(x+5)\quad&&\text{Write the given equation.}\\
(x+1)^2-2(x+5)&=0\quad&&\text{Subtract }2(x+5)\text{ from each side.}\\
x^2+2x+1-2x-10&=0\quad&&\text{Perform calculations.}\\
x^2-9&=0\quad&&\text{Write the equation in standard form.}\\
(x+3)(x-3)&=0\quad&&\text{Factor.}\\
x+3=0&\text{ 0r }x-3=0\quad&&\text{Set each factor equal to }0.\\
x=-3&\text{ or }x=3\quad&&\text{Solve the resulting equations.}
\end{align*}$$
The equation has two solutions: $x=-3$ and $x=3$.
Check the results by substituting them in the original equation:
$$\begin{align*}
x&=-3\\
(-3+1)^2&\stackrel{?}{=}2(-3+5)\\
(-2)^2&\stackrel{?}{=}2(2)\\
4&=4\checkmark\\\\
x&=3\\
(3+1)^2&\stackrel{?}{=}2(3+5)\\
(4)^2&\stackrel{?}{=}2(8)\\
16&=16\checkmark.
\end{align*}$$
Both solutions check the equation.
