x^2+2x-3906=0

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Solution for x^2+2x-3906=0 equation:


Simplifying
x2 + 2x + -3906 = 0

Reorder the terms:
-3906 + 2x + x2 = 0

Solving
-3906 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3906' to each side of the equation.
-3906 + 2x + 3906 + x2 = 0 + 3906

Reorder the terms:
-3906 + 3906 + 2x + x2 = 0 + 3906

Combine like terms: -3906 + 3906 = 0
0 + 2x + x2 = 0 + 3906
2x + x2 = 0 + 3906

Combine like terms: 0 + 3906 = 3906
2x + x2 = 3906

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 = 3906 + 1

Reorder the terms:
1 + 2x + x2 = 3906 + 1

Combine like terms: 3906 + 1 = 3907
1 + 2x + x2 = 3907

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3907

Calculate the square root of the right side: 62.505999712

Break this problem into two subproblems by setting 
(x + 1) equal to 62.505999712 and -62.505999712.

Subproblem 1

x + 1 = 62.505999712 Simplifying x + 1 = 62.505999712 Reorder the terms: 1 + x = 62.505999712 Solving 1 + x = 62.505999712 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 = 62.505999712 + -1 Combine like terms: 1 + -1 = 0 0 + x = 62.505999712 + -1 x = 62.505999712 + -1 Combine like terms: 62.505999712 + -1 = 61.505999712 x = 61.505999712 Simplifying x = 61.505999712

Subproblem 2

x + 1 = -62.505999712 Simplifying x + 1 = -62.505999712 Reorder the terms: 1 + x = -62.505999712 Solving 1 + x = -62.505999712 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 = -62.505999712 + -1 Combine like terms: 1 + -1 = 0 0 + x = -62.505999712 + -1 x = -62.505999712 + -1 Combine like terms: -62.505999712 + -1 = -63.505999712 x = -63.505999712 Simplifying x = -63.505999712

Solution

The solution to the problem is based on the solutions from the subproblems. x = {61.505999712, -63.505999712}

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