x^2+2x+6-2016=0

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Solution for x^2+2x+6-2016=0 equation:


Simplifying
x2 + 2x + 6 + -2016 = 0

Reorder the terms:
6 + -2016 + 2x + x2 = 0

Combine like terms: 6 + -2016 = -2010
-2010 + 2x + x2 = 0

Solving
-2010 + 2x + 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 + 2x + 2010 + x2 = 0 + 2010

Reorder the terms:
-2010 + 2010 + 2x + x2 = 0 + 2010

Combine like terms: -2010 + 2010 = 0
0 + 2x + x2 = 0 + 2010
2x + x2 = 0 + 2010

Combine like terms: 0 + 2010 = 2010
2x + x2 = 2010

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 2010 + 1

Reorder the terms:
1 + 2x + x2 = 2010 + 1

Combine like terms: 2010 + 1 = 2011
1 + 2x + x2 = 2011

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2011

Calculate the square root of the right side: 44.84417465

Break this problem into two subproblems by setting 
(x + 1) equal to 44.84417465 and -44.84417465.

Subproblem 1

x + 1 = 44.84417465 Simplifying x + 1 = 44.84417465 Reorder the terms: 1 + x = 44.84417465 Solving 1 + x = 44.84417465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 44.84417465 + -1 Combine like terms: 1 + -1 = 0 0 + x = 44.84417465 + -1 x = 44.84417465 + -1 Combine like terms: 44.84417465 + -1 = 43.84417465 x = 43.84417465 Simplifying x = 43.84417465

Subproblem 2

x + 1 = -44.84417465 Simplifying x + 1 = -44.84417465 Reorder the terms: 1 + x = -44.84417465 Solving 1 + x = -44.84417465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -44.84417465 + -1 Combine like terms: 1 + -1 = 0 0 + x = -44.84417465 + -1 x = -44.84417465 + -1 Combine like terms: -44.84417465 + -1 = -45.84417465 x = -45.84417465 Simplifying x = -45.84417465

Solution

The solution to the problem is based on the solutions from the subproblems. x = {43.84417465, -45.84417465}

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