Step-by-step explanation:
x² + 5x - 5 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 5
c = -5
x = (-5 ± sqrt(25 - 4×1×-5))/(2×1) =
= (-5 ± sqrt(25 + 20))/2 = (-5 ± sqrt(45))/2 =
= (-5 ± sqrt(9×5))/2 = (-5 ± 3×sqrt(5))/2
x1 = (-5 + 3×sqrt(5))/2 = 0.854101966...
x2 = (-5 - 3×sqrt(5))/2 = -5.854101966...
the solution set is {x1, x2}
