x^2-5x-1=0 is? Answer is 5+√29|2.How to solve?

Answer 1

the quadratic formula:

x = (5±√(5^2+4))/2 = (5±√29)/2

To see how this comes about, follow the logic:

x^2-5x-1 = 0
x^2 - 5x = 1
x^2 - 2(5/2)x + (5/2)^2 = 1 + (5/2)^2
(x - 5/2)^2 = 1 + 25/4
(x - 5/2)^2 = 29/4
x - 5/2 = ±√(29/4)
x = 5/2 ±√29/2
x = (5±√29)/2