x^2+2016x+2017=0

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Solution for x^2+2016x+2017=0 equation: 


Simplifying
x2 + 2016x + 2017 = 0

Reorder the terms:
2017 + 2016x + x2 = 0

Solving
2017 + 2016x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2017' to each side of the equation.
2017 + 2016x + -2017 + x2 = 0 + -2017

Reorder the terms:
2017 + -2017 + 2016x + x2 = 0 + -2017

Combine like terms: 2017 + -2017 = 0
0 + 2016x + x2 = 0 + -2017
2016x + x2 = 0 + -2017

Combine like terms: 0 + -2017 = -2017
2016x + x2 = -2017

The x term is 2016x.  Take half its coefficient (1008).
Square it (1016064) and add it to both sides.

Add '1016064' to each side of the equation.
2016x + 1016064 + x2 = -2017 + 1016064

Reorder the terms:
1016064 + 2016x + x2 = -2017 + 1016064

Combine like terms: -2017 + 1016064 = 1014047
1016064 + 2016x + x2 = 1014047

Factor a perfect square on the left side:
(x + 1008)(x + 1008) = 1014047

Calculate the square root of the right side: 1006.999006951

Break this problem into two subproblems by setting 
(x + 1008) equal to 1006.999006951 and -1006.999006951.


Subproblem 1
x + 1008 = 1006.999006951

Simplifying
x + 1008 = 1006.999006951

Reorder the terms:
1008 + x = 1006.999006951

Solving
1008 + x = 1006.999006951

Solving for variable 'x'.

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

Add '-1008' to each side of the equation.
1008 + -1008 + x = 1006.999006951 + -1008

Combine like terms: 1008 + -1008 = 0
0 + x = 1006.999006951 + -1008
x = 1006.999006951 + -1008

Combine like terms: 1006.999006951 + -1008 = -1.000993049
x = -1.000993049

Simplifying
x = -1.000993049


Subproblem 2
x + 1008 = -1006.999006951

Simplifying
x + 1008 = -1006.999006951

Reorder the terms:
1008 + x = -1006.999006951

Solving
1008 + x = -1006.999006951

Solving for variable 'x'.

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

Add '-1008' to each side of the equation.
1008 + -1008 + x = -1006.999006951 + -1008

Combine like terms: 1008 + -1008 = 0
0 + x = -1006.999006951 + -1008
x = -1006.999006951 + -1008

Combine like terms: -1006.999006951 + -1008 = -2014.999006951
x = -2014.999006951

Simplifying
x = -2014.999006951


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.000993049, -2014.999006951}

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