x² - 11x -1 = 0
⇔ x² - 11x + $\frac{121}{4}$ - $\frac{125}{4}$ = 0
⇔ ( x - $\frac{11}{2}$ ) $^{2}$ - $\frac{125}{4}$ = 0
⇔ ( x - $\frac{11}{2}$ ) $^{2}$ = $\frac{125}{4}$
⇔ x - $\frac{11}{2}$ = ±$\sqrt[2]{\frac{125}{4}}$
⇔ x = ±$\frac{5√5}{2}$ + $\frac{11}{2}$
⇔\(\left[ \begin{array}{l}x=\frac{5√5+11}{2} \\x=\frac{5√5-11}{2}\end{array} \right.\)