d^2-4d-2=0

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Solution for d^2-4d-2=0 equation: 


Simplifying
d2 + -4d + -2 = 0

Reorder the terms:
-2 + -4d + d2 = 0

Solving
-2 + -4d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4d + 2 + d2 = 0 + 2

Reorder the terms:
-2 + 2 + -4d + d2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4d + d2 = 0 + 2
-4d + d2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4d + d2 = 2

The d term is -4d.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4d + 4 + d2 = 2 + 4

Reorder the terms:
4 + -4d + d2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4d + d2 = 6

Factor a perfect square on the left side:
(d + -2)(d + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(d + -2) equal to 2.449489743 and -2.449489743.


Subproblem 1
d + -2 = 2.449489743

Simplifying
d + -2 = 2.449489743

Reorder the terms:
-2 + d = 2.449489743

Solving
-2 + d = 2.449489743

Solving for variable 'd'.

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

Add '2' to each side of the equation.
-2 + 2 + d = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + d = 2.449489743 + 2
d = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
d = 4.449489743

Simplifying
d = 4.449489743


Subproblem 2
d + -2 = -2.449489743

Simplifying
d + -2 = -2.449489743

Reorder the terms:
-2 + d = -2.449489743

Solving
-2 + d = -2.449489743

Solving for variable 'd'.

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

Add '2' to each side of the equation.
-2 + 2 + d = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + d = -2.449489743 + 2
d = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
d = -0.449489743

Simplifying
d = -0.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {4.449489743, -0.449489743}

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