d^2-3d-1=0

Solution for d^2-3d-1=0 equation:

Simplifying
d2 + -3d + -1 = 0

Reorder the terms:
-1 + -3d + d2 = 0

Solving
-1 + -3d + 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 + -3d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + -3d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3d + d2 = 0 + 1
-3d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3d + d2 = 1

The d term is -3d.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3d + 2.25 + d2 = 1 + 2.25

Reorder the terms:
2.25 + -3d + d2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3d + d2 = 3.25

Factor a perfect square on the left side:
(d + -1.5)(d + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(d + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
d + -1.5 = 1.802775638

Simplifying
d + -1.5 = 1.802775638

Reorder the terms:
-1.5 + d = 1.802775638

Solving
-1.5 + d = 1.802775638

Solving for variable 'd'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + d = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + d = 1.802775638 + 1.5
d = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
d = 3.302775638

Simplifying
d = 3.302775638

Subproblem 2
d + -1.5 = -1.802775638

Simplifying
d + -1.5 = -1.802775638

Reorder the terms:
-1.5 + d = -1.802775638

Solving
-1.5 + d = -1.802775638

Solving for variable 'd'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + d = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + d = -1.802775638 + 1.5
d = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
d = -0.302775638

Simplifying
d = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {3.302775638, -0.302775638}