[tex] \bf x-5=\sqrt{-2x+18}\implies \stackrel{\textit{squaring both sides}}{(x-5)^2=-2x+18}
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\stackrel{FOIL}{x^2-10x+25}=-2x+18\implies x^2-8x+7=0
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(x-7)(x-1)=0\implies x=
\begin{cases}
\boxed{7}\\
1
\end{cases}\\\\
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\stackrel{\textit{using x = 1}}{1-5=\sqrt{-2(1)+18}}\implies -4=\sqrt{16}\implies -4\ne 4\quad \otimes
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\stackrel{\textit{using x = 7}}{7-5=\sqrt{-2(7)+18}}\implies 2=\sqrt{4}\implies 2=2\quad \checkmark [/tex]
