d^2-2d-43=0

Solution for d^2-2d-43=0 equation:

Simplifying
d2 + -2d + -43 = 0

Reorder the terms:
-43 + -2d + d2 = 0

Solving
-43 + -2d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -2d + 43 + d2 = 0 + 43

Reorder the terms:
-43 + 43 + -2d + d2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -2d + d2 = 0 + 43
-2d + d2 = 0 + 43

Combine like terms: 0 + 43 = 43
-2d + d2 = 43

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 = 43 + 1

Reorder the terms:
1 + -2d + d2 = 43 + 1

Combine like terms: 43 + 1 = 44
1 + -2d + d2 = 44

Factor a perfect square on the left side:
(d + -1)(d + -1) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(d + -1) equal to 6.633249581 and -6.633249581.

Subproblem 1
d + -1 = 6.633249581

Simplifying
d + -1 = 6.633249581

Reorder the terms:
-1 + d = 6.633249581

Solving
-1 + d = 6.633249581

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 = 6.633249581 + 1

Combine like terms: -1 + 1 = 0
0 + d = 6.633249581 + 1
d = 6.633249581 + 1

Combine like terms: 6.633249581 + 1 = 7.633249581
d = 7.633249581

Simplifying
d = 7.633249581

Subproblem 2
d + -1 = -6.633249581

Simplifying
d + -1 = -6.633249581

Reorder the terms:
-1 + d = -6.633249581

Solving
-1 + d = -6.633249581

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 = -6.633249581 + 1

Combine like terms: -1 + 1 = 0
0 + d = -6.633249581 + 1
d = -6.633249581 + 1

Combine like terms: -6.633249581 + 1 = -5.633249581
d = -5.633249581

Simplifying
d = -5.633249581

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {7.633249581, -5.633249581}