(4x -1)^2 = 11 expand the left side....
16x^2 - 8x + 1 = 11 subtract 11 from both sides
16x^2 - 8x - 10 = 0 divide through by 2
8x^2 - 4x - 5 = 0 this does not factor...using the on-site solver, we get.....
$${\mathtt{8}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{11}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{4}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{11}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{{\mathtt{4}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.579\: \!156\: \!197\: \!588\: \!85}}\\
{\mathtt{x}} = {\mathtt{1.079\: \!156\: \!197\: \!588\: \!85}}\\
\end{array} \right\}$$
Note......we could have also used the square root property to solve this, if we wished.....!!!!!
(4x -1)^2 = 11 expand the left side....
16x^2 - 8x + 1 = 11 subtract 11 from both sides
16x^2 - 8x - 10 = 0 divide through by 2
8x^2 - 4x - 5 = 0 this does not factor...using the on-site solver, we get.....
$${\mathtt{8}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{11}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{4}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{11}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{{\mathtt{4}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.579\: \!156\: \!197\: \!588\: \!85}}\\
{\mathtt{x}} = {\mathtt{1.079\: \!156\: \!197\: \!588\: \!85}}\\
\end{array} \right\}$$
Note......we could have also used the square root property to solve this, if we wished.....!!!!!