\(\sqrt{4x^2-4x+9}=3\)
\(\Leftrightarrow4x^2-4x+9=9\)
\(\Leftrightarrow4x^2-4x=0\)
\(\Leftrightarrow4x\left(x-1\right)=0\)
<=>\(\left[{}\begin{matrix}4x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
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