x^2-xk-1=0

Solution for x^2-xk-1=0 equation:

Simplifying
x2 + -1xk + -1 = 0

Reorder the terms:
-1 + -1kx + x2 = 0

Solving
-1 + -1kx + x2 = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + -1kx + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1kx + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1kx + x2 = 0 + 1
-1kx + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1kx + x2 = 1

Add '-1x2' to each side of the equation.
-1kx + x2 + -1x2 = 1 + -1x2

Combine like terms: x2 + -1x2 = 0
-1kx + 0 = 1 + -1x2
-1kx = 1 + -1x2

Divide each side by '-1x'.
k = -1x-1 + x

Simplifying
k = -1x-1 + x