-d^2-3d-1=0

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


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

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

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

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 3d + d2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + 3d + d2)' equal to zero and attempt to solve:

Simplifying
1 + 3d + d2 = 0

Solving
1 + 3d + d2 = 0

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 = 1.25
2.25 + 3d + d2 = 1.25

Factor a perfect square on the left side:
(d + 1.5)(d + 1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(d + 1.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
d + 1.5 = 1.118033989

Simplifying
d + 1.5 = 1.118033989

Reorder the terms:
1.5 + d = 1.118033989

Solving
1.5 + d = 1.118033989

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 = 1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + d = 1.118033989 + -1.5
d = 1.118033989 + -1.5

Combine like terms: 1.118033989 + -1.5 = -0.381966011
d = -0.381966011

Simplifying
d = -0.381966011


Subproblem 2
d + 1.5 = -1.118033989

Simplifying
d + 1.5 = -1.118033989

Reorder the terms:
1.5 + d = -1.118033989

Solving
1.5 + d = -1.118033989

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 = -1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + d = -1.118033989 + -1.5
d = -1.118033989 + -1.5

Combine like terms: -1.118033989 + -1.5 = -2.618033989
d = -2.618033989

Simplifying
d = -2.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.381966011, -2.618033989}
Solution
d = {-0.381966011, -2.618033989}

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