d^2-6d-1=0

Solution for d^2-6d-1=0 equation:

Simplifying
d2 + -6d + -1 = 0

Reorder the terms:
-1 + -6d + d2 = 0

Solving
-1 + -6d + 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 + -6d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + -6d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6d + d2 = 0 + 1
-6d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6d + d2 = 1

The d term is -6d.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6d + 9 + d2 = 1 + 9

Reorder the terms:
9 + -6d + d2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + -6d + d2 = 10

Factor a perfect square on the left side:
(d + -3)(d + -3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(d + -3) equal to 3.16227766 and -3.16227766.

Subproblem 1
d + -3 = 3.16227766

Simplifying
d + -3 = 3.16227766

Reorder the terms:
-3 + d = 3.16227766

Solving
-3 + d = 3.16227766

Solving for variable 'd'.

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

Add '3' to each side of the equation.
-3 + 3 + d = 3.16227766 + 3

Combine like terms: -3 + 3 = 0
0 + d = 3.16227766 + 3
d = 3.16227766 + 3

Combine like terms: 3.16227766 + 3 = 6.16227766
d = 6.16227766

Simplifying
d = 6.16227766

Subproblem 2
d + -3 = -3.16227766

Simplifying
d + -3 = -3.16227766

Reorder the terms:
-3 + d = -3.16227766

Solving
-3 + d = -3.16227766

Solving for variable 'd'.

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

Add '3' to each side of the equation.
-3 + 3 + d = -3.16227766 + 3

Combine like terms: -3 + 3 = 0
0 + d = -3.16227766 + 3
d = -3.16227766 + 3

Combine like terms: -3.16227766 + 3 = -0.16227766
d = -0.16227766

Simplifying
d = -0.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {6.16227766, -0.16227766}