-d^2-d+1=0

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

Simplifying
-1d2 + -1d + 1 = 0

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

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

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + d + d2 = 0

Move the constant term to the right:

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

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

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

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

The d term is d.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + d2 = 1 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + d2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
1.25 + d2 = 1.25

Factor a perfect square on the left side:
(d + 0.5)(d + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(d + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
d + 0.5 = 1.118033989

Simplifying
d + 0.5 = 1.118033989

Reorder the terms:
0.5 + d = 1.118033989

Solving
0.5 + d = 1.118033989

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = 1.118033989 + -0.5
d = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
d = 0.618033989

Simplifying
d = 0.618033989

Subproblem 2
d + 0.5 = -1.118033989

Simplifying
d + 0.5 = -1.118033989

Reorder the terms:
0.5 + d = -1.118033989

Solving
0.5 + d = -1.118033989

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = -1.118033989 + -0.5
d = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
d = -1.618033989

Simplifying
d = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.618033989, -1.618033989}