$\sqrt{ 4-x }=x+2$
Square both sides of the equation$4-x={x}^{2}+4x+4$
Cancel equal terms on both sides of the equation$-x={x}^{2}+4x$
Move the variables to the left-hand side and change their signs$-x-{x}^{2}-4x=0$
Collect like terms$-5x-{x}^{2}=0$
Factor out $-x$ from the expression$-x \times \left( 5+x \right)=0$
Change the signs on both sides of the equation$x \times \left( 5+x \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }x=0,\\5+x=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=0,\\x=-5\end{array}$
Check if the given value is the solution of the equation$\begin{array} { l }0+2=\sqrt{ 4-0 },\\x=-5\end{array}$
Check if the given value is the solution of the equation$\begin{array} { l }0+2=\sqrt{ 4-0 },\\-5+2=\sqrt{ 4-\left( -5 \right) }\end{array}$
Simplify the expression$\begin{array} { l }2=2,\\-5+2=\sqrt{ 4-\left( -5 \right) }\end{array}$
Simplify the expression$\begin{array} { l }2=2,\\-3=3\end{array}$
The equality is true, therefore $x=0$ is a solution of the equation$\begin{array} { l }x=0,\\-3=3\end{array}$
The equality is false, therefore $x=-5$ is not a solution of the equation$\begin{array} { l }x=0,\\x≠-5\end{array}$
The equation has one solution$x=0$