d^2-2d-5=0

Solution for d^2-2d-5=0 equation:

Simplifying
d2 + -2d + -5 = 0

Reorder the terms:
-5 + -2d + d2 = 0

Solving
-5 + -2d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2d + 5 + d2 = 0 + 5

Reorder the terms:
-5 + 5 + -2d + d2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2d + d2 = 0 + 5
-2d + d2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2d + d2 = 5

The d term is -2d.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2d + 1 + d2 = 5 + 1

Reorder the terms:
1 + -2d + d2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2d + d2 = 6

Factor a perfect square on the left side:
(d + -1)(d + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(d + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
d + -1 = 2.449489743

Simplifying
d + -1 = 2.449489743

Reorder the terms:
-1 + d = 2.449489743

Solving
-1 + d = 2.449489743

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + d = 2.449489743 + 1
d = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
d = 3.449489743

Simplifying
d = 3.449489743

Subproblem 2
d + -1 = -2.449489743

Simplifying
d + -1 = -2.449489743

Reorder the terms:
-1 + d = -2.449489743

Solving
-1 + d = -2.449489743

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + d = -2.449489743 + 1
d = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
d = -1.449489743

Simplifying
d = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {3.449489743, -1.449489743}