Solve for: x+2=sqrt(4-x)

Expression: $x+2=\sqrt{ 4-x }$

Swap the sides of the equation

$\sqrt{ 4-x }=x+2$

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

$x=0$