Answer:
[tex]\boxed{x_1 = \frac{7 + \sqrt{5} }{2} ~~or~~x_2 = \frac{7 - \sqrt{5} }{2} }[/tex]
Step-by-step explanation:
[tex]x^2 - 7x + 11 = 0[/tex]
[tex]x^2 - 7x = -11[/tex]
[tex](x - \frac{7}{2} )^2 - \frac{49}{4} = -11[/tex]
[tex](x - \frac{7}{2} )^2 = -11 + \frac{49}{4}[/tex]
[tex](x - \frac{7}{2} )^2 = \frac{5}{4}[/tex]
[tex]x - \frac{7}{2} = \pm \sqrt{\frac{5}{4}}[/tex]
[tex]x = \frac{7 \pm \sqrt{5} }{2}[/tex]
