2687.24D^2-12933.92D-13760.26=0

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Solution for 2687.24D^2-12933.92D-13760.26=0 equation: 


Simplifying
2687.24D2 + -12933.92D + -13760.26 = 0

Reorder the terms:
-13760.26 + -12933.92D + 2687.24D2 = 0

Solving
-13760.26 + -12933.92D + 2687.24D2 = 0

Solving for variable 'D'.

Begin completing the square.  Divide all terms by
2687.24 the coefficient of the squared term: 

Divide each side by '2687.24'.
-5.120592132 + -4.813087034D + D2 = 0

Move the constant term to the right:

Add '5.120592132' to each side of the equation.
-5.120592132 + -4.813087034D + 5.120592132 + D2 = 0 + 5.120592132

Reorder the terms:
-5.120592132 + 5.120592132 + -4.813087034D + D2 = 0 + 5.120592132

Combine like terms: -5.120592132 + 5.120592132 = 0.000000000
0.000000000 + -4.813087034D + D2 = 0 + 5.120592132
-4.813087034D + D2 = 0 + 5.120592132

Combine like terms: 0 + 5.120592132 = 5.120592132
-4.813087034D + D2 = 5.120592132

The D term is -4.813087034D.  Take half its coefficient (-2.406543517).
Square it (5.791451699) and add it to both sides.

Add '5.791451699' to each side of the equation.
-4.813087034D + 5.791451699 + D2 = 5.120592132 + 5.791451699

Reorder the terms:
5.791451699 + -4.813087034D + D2 = 5.120592132 + 5.791451699

Combine like terms: 5.120592132 + 5.791451699 = 10.912043831
5.791451699 + -4.813087034D + D2 = 10.912043831

Factor a perfect square on the left side:
(D + -2.406543517)(D + -2.406543517) = 10.912043831

Calculate the square root of the right side: 3.303338286

Break this problem into two subproblems by setting 
(D + -2.406543517) equal to 3.303338286 and -3.303338286.


Subproblem 1
D + -2.406543517 = 3.303338286

Simplifying
D + -2.406543517 = 3.303338286

Reorder the terms:
-2.406543517 + D = 3.303338286

Solving
-2.406543517 + D = 3.303338286

Solving for variable 'D'.

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

Add '2.406543517' to each side of the equation.
-2.406543517 + 2.406543517 + D = 3.303338286 + 2.406543517

Combine like terms: -2.406543517 + 2.406543517 = 0.000000000
0.000000000 + D = 3.303338286 + 2.406543517
D = 3.303338286 + 2.406543517

Combine like terms: 3.303338286 + 2.406543517 = 5.709881803
D = 5.709881803

Simplifying
D = 5.709881803


Subproblem 2
D + -2.406543517 = -3.303338286

Simplifying
D + -2.406543517 = -3.303338286

Reorder the terms:
-2.406543517 + D = -3.303338286

Solving
-2.406543517 + D = -3.303338286

Solving for variable 'D'.

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

Add '2.406543517' to each side of the equation.
-2.406543517 + 2.406543517 + D = -3.303338286 + 2.406543517

Combine like terms: -2.406543517 + 2.406543517 = 0.000000000
0.000000000 + D = -3.303338286 + 2.406543517
D = -3.303338286 + 2.406543517

Combine like terms: -3.303338286 + 2.406543517 = -0.896794769
D = -0.896794769

Simplifying
D = -0.896794769


Solution
The solution to the problem is based on the solutions
from the subproblems.
D = {5.709881803, -0.896794769}

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