d^2-1=5d

Solution for d^2-1=5d equation:

Simplifying
d2 + -1 = 5d

Reorder the terms:
-1 + d2 = 5d

Solving
-1 + d2 = 5d

Solving for variable 'd'.

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

Combine like terms: 5d + -5d = 0
-1 + -5d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + -5d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5d + d2 = 0 + 1
-5d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5d + d2 = 1

The d term is -5d.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5d + 6.25 + d2 = 1 + 6.25

Reorder the terms:
6.25 + -5d + d2 = 1 + 6.25

Combine like terms: 1 + 6.25 = 7.25
6.25 + -5d + d2 = 7.25

Factor a perfect square on the left side:
(d + -2.5)(d + -2.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(d + -2.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
d + -2.5 = 2.692582404

Simplifying
d + -2.5 = 2.692582404

Reorder the terms:
-2.5 + d = 2.692582404

Solving
-2.5 + d = 2.692582404

Solving for variable 'd'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + d = 2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + d = 2.692582404 + 2.5
d = 2.692582404 + 2.5

Combine like terms: 2.692582404 + 2.5 = 5.192582404
d = 5.192582404

Simplifying
d = 5.192582404

Subproblem 2
d + -2.5 = -2.692582404

Simplifying
d + -2.5 = -2.692582404

Reorder the terms:
-2.5 + d = -2.692582404

Solving
-2.5 + d = -2.692582404

Solving for variable 'd'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + d = -2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + d = -2.692582404 + 2.5
d = -2.692582404 + 2.5

Combine like terms: -2.692582404 + 2.5 = -0.192582404
d = -0.192582404

Simplifying
d = -0.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {5.192582404, -0.192582404}