Answer:
33
Step-by-step explanation:
[tex] {x}^{2} - 5x - 2 = 0 \\ \\ equating \: it \: with \\ a {x}^{2} + bx + c = 0 \\ we \: find : \\ a = 1 \\ b = - 5 \\ c = - 2 \\ \\ {b}^{2} - 4ac \\ = {( - 5)}^{2} - 4 \times 1( - 2) \\ = 25 + 8 \\ = 33 \\ \\ by \: quadratic \: formula \\ \\ x = \frac{ - b \pm \sqrt{ {b}^{2} -4ac } }{2a} \\ \\ x = \frac{ - ( - 5) \pm \sqrt{33}}{2 \times 1} \\ \\ x = \frac{ 5 \pm \sqrt{33}}{2}...(1) \\ \\x = \frac{ 5 \pm \sqrt{n}}{2}...(2) (given)\\ \\ equating \: equations \: (1) \: and \: (2) \\ \\ \huge \red{ \boxed{n = 33}}[/tex]
