d^2-2d-1=0

Solution for d^2-2d-1=0 equation:

Simplifying
d2 + -2d + -1 = 0

Reorder the terms:
-1 + -2d + d2 = 0

Solving
-1 + -2d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + -2d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2d + d2 = 0 + 1
-2d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2d + d2 = 1

The d term is -2d.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2d + 1 + d2 = 1 + 1

Reorder the terms:
1 + -2d + d2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + -2d + d2 = 2

Factor a perfect square on the left side:
(d + -1)(d + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(d + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
d + -1 = 1.414213562

Simplifying
d + -1 = 1.414213562

Reorder the terms:
-1 + d = 1.414213562

Solving
-1 + d = 1.414213562

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + d = 1.414213562 + 1
d = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
d = 2.414213562

Simplifying
d = 2.414213562

Subproblem 2
d + -1 = -1.414213562

Simplifying
d + -1 = -1.414213562

Reorder the terms:
-1 + d = -1.414213562

Solving
-1 + d = -1.414213562

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + d = -1.414213562 + 1
d = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
d = -0.414213562

Simplifying
d = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.414213562, -0.414213562}