Answer
$\{16\}$
Work Step by Step
We are given the quadratic equation:
$$(1+\sqrt x)^2-2(1+\sqrt x)-15=0.$$
Rewrite the equation by building a perfect square and solve it:
$$\begin{align*}
[(1+\sqrt x)^2-2(1+\sqrt x)+1]-1-15&=0\\
(1+\sqrt x-1)^2&=16\\
(\sqrt x)^2&=16\\
x&=16.
\end{align*}$$
Check the solution:
$$\begin{align*}
x&=16\\
(1+\sqrt{16})^2-2(1+\sqrt{16})-15&\stackrel{?}{=}0\\
(1+4)^2-2(1+4)-15&\stackrel{?}{=}0\\
25-10-15&\stackrel{?}{=}0\\
0&=0\checkmark.
\end{align*}$$
So the solution set of the given equation is $\{16\}$.
