\(\left(x-4\right)^2-9=0\)
\(\Leftrightarrow\left(x-4\right)^2-3^2=0\)
\(\Leftrightarrow\left(x-4-3\right)\left(x-4+3\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=1\end{matrix}\right.\)
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