D^2+520D-5200=0

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Solution for D^2+520D-5200=0 equation: 


Simplifying
D2 + 520D + -5200 = 0

Reorder the terms:
-5200 + 520D + D2 = 0

Solving
-5200 + 520D + D2 = 0

Solving for variable 'D'.

Begin completing the square.

Move the constant term to the right:

Add '5200' to each side of the equation.
-5200 + 520D + 5200 + D2 = 0 + 5200

Reorder the terms:
-5200 + 5200 + 520D + D2 = 0 + 5200

Combine like terms: -5200 + 5200 = 0
0 + 520D + D2 = 0 + 5200
520D + D2 = 0 + 5200

Combine like terms: 0 + 5200 = 5200
520D + D2 = 5200

The D term is 520D.  Take half its coefficient (260).
Square it (67600) and add it to both sides.

Add '67600' to each side of the equation.
520D + 67600 + D2 = 5200 + 67600

Reorder the terms:
67600 + 520D + D2 = 5200 + 67600

Combine like terms: 5200 + 67600 = 72800
67600 + 520D + D2 = 72800

Factor a perfect square on the left side:
(D + 260)(D + 260) = 72800

Calculate the square root of the right side: 269.814751265

Break this problem into two subproblems by setting 
(D + 260) equal to 269.814751265 and -269.814751265.


Subproblem 1
D + 260 = 269.814751265

Simplifying
D + 260 = 269.814751265

Reorder the terms:
260 + D = 269.814751265

Solving
260 + D = 269.814751265

Solving for variable 'D'.

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

Add '-260' to each side of the equation.
260 + -260 + D = 269.814751265 + -260

Combine like terms: 260 + -260 = 0
0 + D = 269.814751265 + -260
D = 269.814751265 + -260

Combine like terms: 269.814751265 + -260 = 9.814751265
D = 9.814751265

Simplifying
D = 9.814751265


Subproblem 2
D + 260 = -269.814751265

Simplifying
D + 260 = -269.814751265

Reorder the terms:
260 + D = -269.814751265

Solving
260 + D = -269.814751265

Solving for variable 'D'.

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

Add '-260' to each side of the equation.
260 + -260 + D = -269.814751265 + -260

Combine like terms: 260 + -260 = 0
0 + D = -269.814751265 + -260
D = -269.814751265 + -260

Combine like terms: -269.814751265 + -260 = -529.814751265
D = -529.814751265

Simplifying
D = -529.814751265


Solution
The solution to the problem is based on the solutions
from the subproblems.
D = {9.814751265, -529.814751265}

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