Answer
$x=\displaystyle \frac{5}{2}\pm\frac{\sqrt{21}}{2}$
Work Step by Step
We complete the square:
$x^{2}-5x+1=0$
$x^{2}-5x=-1$
$x^{2}-5x+\frac{25}{4}=-1+\frac{25}{4}=-\frac{4}{4}+\frac{25}{4}=\frac{21}{4}$
$(x-\frac{5}{2})^{2}=\frac{21}{4}$
$x-\frac{5}{2}=\pm\sqrt{\frac{21}{4}}=\pm\frac{\sqrt{21}}{2}$
$x=\displaystyle \frac{5}{2}\pm\frac{\sqrt{21}}{2}$
