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Question

# Solve the equation. Write all proposed solutions. Cross out those that are extraneous.$\sqrt { 9 - a } - a = 3$

Solution

Verified
Step 1
1 of 3

Evaluating the given radical equation, we,

\begin{aligned} \sqrt{9-a}&=3+a&&\texttt{Add a both sides}\\(\sqrt{9-a})^{2}&=(a+3)^{2}&&\texttt{Square both sides}\\9-a&=a^{2}+6a+9&&\texttt{Expand the perfect square}\\0&=a^{2}+7a&&\texttt{Add a and -9 both sides}\\0&=a(a+7)&&\texttt{Factor}\\a=0~~~~ &\texttt{or}~~~~a+7=0&&\texttt{Set each factor equal to 0}\\a=0~~~~&\texttt{or}~~~~a=-7 \end{aligned}

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