2d^2+4000d-2011627=0

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Solution for 2d^2+4000d-2011627=0 equation:


Simplifying
2d2 + 4000d + -2011627 = 0

Reorder the terms:
-2011627 + 4000d + 2d2 = 0

Solving
-2011627 + 4000d + 2d2 = 0

Solving for variable 'd'.

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

Divide each side by '2'.
-1005813.5 + 2000d + d2 = 0

Move the constant term to the right:

Add '1005813.5' to each side of the equation.
-1005813.5 + 2000d + 1005813.5 + d2 = 0 + 1005813.5

Reorder the terms:
-1005813.5 + 1005813.5 + 2000d + d2 = 0 + 1005813.5

Combine like terms: -1005813.5 + 1005813.5 = 0.0
0.0 + 2000d + d2 = 0 + 1005813.5
2000d + d2 = 0 + 1005813.5

Combine like terms: 0 + 1005813.5 = 1005813.5
2000d + d2 = 1005813.5

The d term is 2000d.  Take half its coefficient (1000).
Square it (1000000) and add it to both sides.

Add '1000000' to each side of the equation.
2000d + 1000000 + d2 = 1005813.5 + 1000000

Reorder the terms:
1000000 + 2000d + d2 = 1005813.5 + 1000000

Combine like terms: 1005813.5 + 1000000 = 2005813.5
1000000 + 2000d + d2 = 2005813.5

Factor a perfect square on the left side:
(d + 1000)(d + 1000) = 2005813.5

Calculate the square root of the right side: 1416.267453555

Break this problem into two subproblems by setting 
(d + 1000) equal to 1416.267453555 and -1416.267453555.


Subproblem 1
d + 1000 = 1416.267453555

Simplifying
d + 1000 = 1416.267453555

Reorder the terms:
1000 + d = 1416.267453555

Solving
1000 + d = 1416.267453555

Solving for variable 'd'.

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

Add '-1000' to each side of the equation.
1000 + -1000 + d = 1416.267453555 + -1000

Combine like terms: 1000 + -1000 = 0
0 + d = 1416.267453555 + -1000
d = 1416.267453555 + -1000

Combine like terms: 1416.267453555 + -1000 = 416.267453555
d = 416.267453555

Simplifying
d = 416.267453555


Subproblem 2
d + 1000 = -1416.267453555

Simplifying
d + 1000 = -1416.267453555

Reorder the terms:
1000 + d = -1416.267453555

Solving
1000 + d = -1416.267453555

Solving for variable 'd'.

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

Add '-1000' to each side of the equation.
1000 + -1000 + d = -1416.267453555 + -1000

Combine like terms: 1000 + -1000 = 0
0 + d = -1416.267453555 + -1000
d = -1416.267453555 + -1000

Combine like terms: -1416.267453555 + -1000 = -2416.267453555
d = -2416.267453555

Simplifying
d = -2416.267453555


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {416.267453555, -2416.267453555}

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