2272.38(D*D)-2(6048.75)D-4291.18=0

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Solution for 2272.38(D*D)-2(6048.75)D-4291.18=0 equation: 


Simplifying
2272.38(D * D) + -2(6048.75) * D + -4291.18 = 0

Multiply D * D
2272.38(D2) + -2(6048.75) * D + -4291.18 = 0

Multiply -2 * 6048.75
2272.38D2 + -12097.5D + -4291.18 = 0

Reorder the terms:
-4291.18 + -12097.5D + 2272.38D2 = 0

Solving
-4291.18 + -12097.5D + 2272.38D2 = 0

Solving for variable 'D'.

Begin completing the square.  Divide all terms by
2272.38 the coefficient of the squared term: 

Divide each side by '2272.38'.
-1.888407749 + -5.323713463D + D2 = 0

Move the constant term to the right:

Add '1.888407749' to each side of the equation.
-1.888407749 + -5.323713463D + 1.888407749 + D2 = 0 + 1.888407749

Reorder the terms:
-1.888407749 + 1.888407749 + -5.323713463D + D2 = 0 + 1.888407749

Combine like terms: -1.888407749 + 1.888407749 = 0.000000000
0.000000000 + -5.323713463D + D2 = 0 + 1.888407749
-5.323713463D + D2 = 0 + 1.888407749

Combine like terms: 0 + 1.888407749 = 1.888407749
-5.323713463D + D2 = 1.888407749

The D term is -5.323713463D.  Take half its coefficient (-2.661856732).
Square it (7.085481262) and add it to both sides.

Add '7.085481262' to each side of the equation.
-5.323713463D + 7.085481262 + D2 = 1.888407749 + 7.085481262

Reorder the terms:
7.085481262 + -5.323713463D + D2 = 1.888407749 + 7.085481262

Combine like terms: 1.888407749 + 7.085481262 = 8.973889011
7.085481262 + -5.323713463D + D2 = 8.973889011

Factor a perfect square on the left side:
(D + -2.661856732)(D + -2.661856732) = 8.973889011

Calculate the square root of the right side: 2.995645008

Break this problem into two subproblems by setting 
(D + -2.661856732) equal to 2.995645008 and -2.995645008.


Subproblem 1
D + -2.661856732 = 2.995645008

Simplifying
D + -2.661856732 = 2.995645008

Reorder the terms:
-2.661856732 + D = 2.995645008

Solving
-2.661856732 + D = 2.995645008

Solving for variable 'D'.

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

Add '2.661856732' to each side of the equation.
-2.661856732 + 2.661856732 + D = 2.995645008 + 2.661856732

Combine like terms: -2.661856732 + 2.661856732 = 0.000000000
0.000000000 + D = 2.995645008 + 2.661856732
D = 2.995645008 + 2.661856732

Combine like terms: 2.995645008 + 2.661856732 = 5.65750174
D = 5.65750174

Simplifying
D = 5.65750174


Subproblem 2
D + -2.661856732 = -2.995645008

Simplifying
D + -2.661856732 = -2.995645008

Reorder the terms:
-2.661856732 + D = -2.995645008

Solving
-2.661856732 + D = -2.995645008

Solving for variable 'D'.

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

Add '2.661856732' to each side of the equation.
-2.661856732 + 2.661856732 + D = -2.995645008 + 2.661856732

Combine like terms: -2.661856732 + 2.661856732 = 0.000000000
0.000000000 + D = -2.995645008 + 2.661856732
D = -2.995645008 + 2.661856732

Combine like terms: -2.995645008 + 2.661856732 = -0.333788276
D = -0.333788276

Simplifying
D = -0.333788276


Solution
The solution to the problem is based on the solutions
from the subproblems.
D = {5.65750174, -0.333788276}

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