\(a,x^2=6\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{6}\\x=-\sqrt{6}\end{matrix}\right.\\ b,x^2+6x+9=25\\ \Leftrightarrow\left(x+3\right)^2-25=0\\ \Leftrightarrow\left(x+3-5\right)\left(x+3+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-8\end{matrix}\right.\\ c,\sqrt{x}< 5\\ \Leftrightarrow0\le x< 25\\ d,\sqrt{9x^2}=2x+1\\ \Leftrightarrow\left[{}\begin{matrix}3x=2x+1\left(x\ge0\right)\\3x=-2x-1\left(x< 0\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-\dfrac{1}{5}\left(tm\right)\end{matrix}\right.\\ e,\sqrt{1-4x+4x^2}=5\Leftrightarrow\sqrt{\left(2x-1\right)^2}=5\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=5\left(x\ge\dfrac{1}{2}\right)\\1-2x=5\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)
