x^2-5x-1=0 is? Answer is 5+√29|2.How to solve?
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
To solve the equation x^2 - 5x - 1 = 0, you can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -5, and c = -1. Substituting these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(1)(-1))) / (2(1))
x = (5 ± √(25 + 4)) / 2
x = (5 ± √29) / 2
Thus, the solutions to the equation x^2 - 5x - 1 = 0 are:
x = (5 + √29) / 2
x = (5 - √29) / 2
Please note that the given answer is only one of the two solutions. The other solution can be obtained by changing the sign in the quadratic formula.