[tex]{x}^{2} - 5x - 13 = 0 \\ ( {x})^{2} - 2(x)( \frac{5}{2} ) + ( \frac{5}{2})^{2} - \frac{77}{4} = 0 \\ {(x - \frac{5}{2} })^{2} - ( \frac{ \sqrt{77} }{2} )^{2} = 0 \\ (x - \frac{5}{2} - \frac{ \sqrt{77} }{2} )(x - \frac{5}{2} + \frac{ \sqrt{77} }{2} ) = 0 \\ (x - (\frac{5}{2} + \frac{ \sqrt{77} }{2}) )(x - ( \frac{5}{2} - \frac{ \sqrt{77} }{2} )) = 0 \\ \: x = \frac{5}{2} + \frac{ \sqrt{77} }{2} \: or \: x = \frac{5}{2} - \frac{ \sqrt{77} }{2}\\ then \: x = \frac{5 + \sqrt{77} }{2} \: or\: x = \frac{5 - \sqrt{77} }{2} [/tex]
