l x^2 - 4x - 5 l = 7 we have two equations here......
The first is :
x^2 - 4x - 5 = 7 subtract 7 from both sides
x^2 - 4x - 12 = 0 factor
(x - 6) ( x + 2) = 0 and, setting each linear factor to 0 means that x= 6 or x = -2
The second equation is :
-(x^2 - 4x - 5) = 7 multiply both sides by -1
x^2 - 4x - 5 = -7 add 7 to both sides
x^2 - 4x + 2 = 0 the solution to this is:
$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{2}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{0.585\: \!786\: \!437\: \!626\: \!905}}\\
{\mathtt{x}} = {\mathtt{3.414\: \!213\: \!562\: \!373\: \!095}}\\
\end{array} \right\}$$
Thus...we have 4 values that make this true....
