3218.41(D^2)-13433.42D-4458.78=0

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Solution for 3218.41(D^2)-13433.42D-4458.78=0 equation: 


Simplifying
3218.41(D2) + -13433.42D + -4458.78 = 0

Reorder the terms:
-4458.78 + -13433.42D + 3218.41D2 = 0

Solving
-4458.78 + -13433.42D + 3218.41D2 = 0

Solving for variable 'D'.

Begin completing the square.  Divide all terms by
3218.41 the coefficient of the squared term: 

Divide each side by '3218.41'.
-1.38539838 + -4.173930605D + D2 = 0

Move the constant term to the right:

Add '1.38539838' to each side of the equation.
-1.38539838 + -4.173930605D + 1.38539838 + D2 = 0 + 1.38539838

Reorder the terms:
-1.38539838 + 1.38539838 + -4.173930605D + D2 = 0 + 1.38539838

Combine like terms: -1.38539838 + 1.38539838 = 0.00000000
0.00000000 + -4.173930605D + D2 = 0 + 1.38539838
-4.173930605D + D2 = 0 + 1.38539838

Combine like terms: 0 + 1.38539838 = 1.38539838
-4.173930605D + D2 = 1.38539838

The D term is -4.173930605D.  Take half its coefficient (-2.086965303).
Square it (4.355424176) and add it to both sides.

Add '4.355424176' to each side of the equation.
-4.173930605D + 4.355424176 + D2 = 1.38539838 + 4.355424176

Reorder the terms:
4.355424176 + -4.173930605D + D2 = 1.38539838 + 4.355424176

Combine like terms: 1.38539838 + 4.355424176 = 5.740822556
4.355424176 + -4.173930605D + D2 = 5.740822556

Factor a perfect square on the left side:
(D + -2.086965303)(D + -2.086965303) = 5.740822556

Calculate the square root of the right side: 2.396001368

Break this problem into two subproblems by setting 
(D + -2.086965303) equal to 2.396001368 and -2.396001368.


Subproblem 1
D + -2.086965303 = 2.396001368

Simplifying
D + -2.086965303 = 2.396001368

Reorder the terms:
-2.086965303 + D = 2.396001368

Solving
-2.086965303 + D = 2.396001368

Solving for variable 'D'.

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

Add '2.086965303' to each side of the equation.
-2.086965303 + 2.086965303 + D = 2.396001368 + 2.086965303

Combine like terms: -2.086965303 + 2.086965303 = 0.000000000
0.000000000 + D = 2.396001368 + 2.086965303
D = 2.396001368 + 2.086965303

Combine like terms: 2.396001368 + 2.086965303 = 4.482966671
D = 4.482966671

Simplifying
D = 4.482966671


Subproblem 2
D + -2.086965303 = -2.396001368

Simplifying
D + -2.086965303 = -2.396001368

Reorder the terms:
-2.086965303 + D = -2.396001368

Solving
-2.086965303 + D = -2.396001368

Solving for variable 'D'.

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

Add '2.086965303' to each side of the equation.
-2.086965303 + 2.086965303 + D = -2.396001368 + 2.086965303

Combine like terms: -2.086965303 + 2.086965303 = 0.000000000
0.000000000 + D = -2.396001368 + 2.086965303
D = -2.396001368 + 2.086965303

Combine like terms: -2.396001368 + 2.086965303 = -0.309036065
D = -0.309036065

Simplifying
D = -0.309036065


Solution
The solution to the problem is based on the solutions
from the subproblems.
D = {4.482966671, -0.309036065}

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