x^2+2x-122=0

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Solution for x^2+2x-122=0 equation:


Simplifying
x2 + 2x + -122 = 0

Reorder the terms:
-122 + 2x + x2 = 0

Solving
-122 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '122' to each side of the equation.
-122 + 2x + 122 + x2 = 0 + 122

Reorder the terms:
-122 + 122 + 2x + x2 = 0 + 122

Combine like terms: -122 + 122 = 0
0 + 2x + x2 = 0 + 122
2x + x2 = 0 + 122

Combine like terms: 0 + 122 = 122
2x + x2 = 122

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 = 122 + 1

Reorder the terms:
1 + 2x + x2 = 122 + 1

Combine like terms: 122 + 1 = 123
1 + 2x + x2 = 123

Factor a perfect square on the left side:
(x + 1)(x + 1) = 123

Calculate the square root of the right side: 11.090536506

Break this problem into two subproblems by setting 
(x + 1) equal to 11.090536506 and -11.090536506.

Subproblem 1

x + 1 = 11.090536506 Simplifying x + 1 = 11.090536506 Reorder the terms: 1 + x = 11.090536506 Solving 1 + x = 11.090536506 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 = 11.090536506 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.090536506 + -1 x = 11.090536506 + -1 Combine like terms: 11.090536506 + -1 = 10.090536506 x = 10.090536506 Simplifying x = 10.090536506

Subproblem 2

x + 1 = -11.090536506 Simplifying x + 1 = -11.090536506 Reorder the terms: 1 + x = -11.090536506 Solving 1 + x = -11.090536506 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 = -11.090536506 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.090536506 + -1 x = -11.090536506 + -1 Combine like terms: -11.090536506 + -1 = -12.090536506 x = -12.090536506 Simplifying x = -12.090536506

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.090536506, -12.090536506}

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