x^2+2010x+2010=0

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Solution for x^2+2010x+2010=0 equation: 


Simplifying
x2 + 2010x + 2010 = 0

Reorder the terms:
2010 + 2010x + x2 = 0

Solving
2010 + 2010x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2010' to each side of the equation.
2010 + 2010x + -2010 + x2 = 0 + -2010

Reorder the terms:
2010 + -2010 + 2010x + x2 = 0 + -2010

Combine like terms: 2010 + -2010 = 0
0 + 2010x + x2 = 0 + -2010
2010x + x2 = 0 + -2010

Combine like terms: 0 + -2010 = -2010
2010x + x2 = -2010

The x term is 2010x.  Take half its coefficient (1005).
Square it (1010025) and add it to both sides.

Add '1010025' to each side of the equation.
2010x + 1010025 + x2 = -2010 + 1010025

Reorder the terms:
1010025 + 2010x + x2 = -2010 + 1010025

Combine like terms: -2010 + 1010025 = 1008015
1010025 + 2010x + x2 = 1008015

Factor a perfect square on the left side:
(x + 1005)(x + 1005) = 1008015

Calculate the square root of the right side: 1003.999501992

Break this problem into two subproblems by setting 
(x + 1005) equal to 1003.999501992 and -1003.999501992.


Subproblem 1
x + 1005 = 1003.999501992

Simplifying
x + 1005 = 1003.999501992

Reorder the terms:
1005 + x = 1003.999501992

Solving
1005 + x = 1003.999501992

Solving for variable 'x'.

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

Add '-1005' to each side of the equation.
1005 + -1005 + x = 1003.999501992 + -1005

Combine like terms: 1005 + -1005 = 0
0 + x = 1003.999501992 + -1005
x = 1003.999501992 + -1005

Combine like terms: 1003.999501992 + -1005 = -1.000498008
x = -1.000498008

Simplifying
x = -1.000498008


Subproblem 2
x + 1005 = -1003.999501992

Simplifying
x + 1005 = -1003.999501992

Reorder the terms:
1005 + x = -1003.999501992

Solving
1005 + x = -1003.999501992

Solving for variable 'x'.

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

Add '-1005' to each side of the equation.
1005 + -1005 + x = -1003.999501992 + -1005

Combine like terms: 1005 + -1005 = 0
0 + x = -1003.999501992 + -1005
x = -1003.999501992 + -1005

Combine like terms: -1003.999501992 + -1005 = -2008.999501992
x = -2008.999501992

Simplifying
x = -2008.999501992


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.000498008, -2008.999501992}

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