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Question

# Solve the equation. Write all proposed solutions. Cross out those that are extraneous.$\sqrt { - x + 2 } + 2 = x$

Solution

Verified
Step 1
1 of 3

Evaluating the given radical equation, we,

\begin{aligned} \sqrt{-x+2}&=x-2&&\texttt{Add -2 both sides}\\(\sqrt{-x+2})^{2}&=(x-2)^{2}&&\texttt{Square both sides}\\-x+2&=x^{2}-4x+4&&\texttt{Expand the perfect square}\\0&=x^{2}-3x+2&&\texttt{Add x and -2 both sides}\\0&=x^{2}-x-2x+2&&\texttt{Rewrite the middle term}\\0&=x(x-1)-2(x-1)\\0&=(x-2)(x-1)&&\texttt{Factor}\\x-2=0~~~~ &\texttt{or}~~~~x-1=0&&\texttt{Set each factor equal to 0}\\x=2~~~~&\texttt{or}~~~~x=1 \end{aligned}

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