d^2=59-23d

Solution for d^2=59-23d equation:

Simplifying
d2 = 59 + -23d

Solving
d2 = 59 + -23d

Solving for variable 'd'.

Reorder the terms:
-59 + 23d + d2 = 59 + -23d + -59 + 23d

Reorder the terms:
-59 + 23d + d2 = 59 + -59 + -23d + 23d

Combine like terms: 59 + -59 = 0
-59 + 23d + d2 = 0 + -23d + 23d
-59 + 23d + d2 = -23d + 23d

Combine like terms: -23d + 23d = 0
-59 + 23d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 23d + 59 + d2 = 0 + 59

Reorder the terms:
-59 + 59 + 23d + d2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 23d + d2 = 0 + 59
23d + d2 = 0 + 59

Combine like terms: 0 + 59 = 59
23d + d2 = 59

The d term is 23d.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23d + 132.25 + d2 = 59 + 132.25

Reorder the terms:
132.25 + 23d + d2 = 59 + 132.25

Combine like terms: 59 + 132.25 = 191.25
132.25 + 23d + d2 = 191.25

Factor a perfect square on the left side:
(d + 11.5)(d + 11.5) = 191.25

Calculate the square root of the right side: 13.829316686

Break this problem into two subproblems by setting 
(d + 11.5) equal to 13.829316686 and -13.829316686.

Subproblem 1
d + 11.5 = 13.829316686

Simplifying
d + 11.5 = 13.829316686

Reorder the terms:
11.5 + d = 13.829316686

Solving
11.5 + d = 13.829316686

Solving for variable 'd'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + d = 13.829316686 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + d = 13.829316686 + -11.5
d = 13.829316686 + -11.5

Combine like terms: 13.829316686 + -11.5 = 2.329316686
d = 2.329316686

Simplifying
d = 2.329316686

Subproblem 2
d + 11.5 = -13.829316686

Simplifying
d + 11.5 = -13.829316686

Reorder the terms:
11.5 + d = -13.829316686

Solving
11.5 + d = -13.829316686

Solving for variable 'd'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + d = -13.829316686 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + d = -13.829316686 + -11.5
d = -13.829316686 + -11.5

Combine like terms: -13.829316686 + -11.5 = -25.329316686
d = -25.329316686

Simplifying
d = -25.329316686

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.329316686, -25.329316686}