Find all complex solutions of X^2-5X -5= 0

ANSWER[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]EXPLANATIONThe given equation is [tex] {x}^{2} - 5x - 5 = 0[/tex]The solution is given by the formula [tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]where a=1, b=-5, c=-5We substitute into the formula to get;[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)( - 5)} }{2(1)} [/tex]We simplify to get,[tex]x = \frac{ 5 \pm \sqrt{ 45} }{2} [/tex]The solutions are:[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]The equation has no complex roots.