`\sqrt{4-x^2}-x+2=0`

#andy

\[\begin{array}{l}
\sqrt {4 - {x^2}}  - x + 2 = 0\\
DKXD:x \ge 2\\
 \Leftrightarrow \sqrt {4 - {x^2}}  = x - 2\\
 \Leftrightarrow 4 - {x^2} = {(x - 2)^2}\\
 \Leftrightarrow 4 - {x^2} = {x^2} - 4x + 4\\
 \Leftrightarrow 4 - {x^2} - {x^2} + 4x - 4 = 0\\
 \Leftrightarrow  - 2{x^2} + 4x = 0\\
 \Leftrightarrow  - 2x(x - 2) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
 - 2x = 0\\
x - 2 = 0
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 0\left( {KTMDK} \right)\\
x = 2\left( {TMDK} \right)
\end{array} \right.\\
 \Rightarrow x = 2
\end{array}\]