x^2+2x-165=0

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Solution for x^2+2x-165=0 equation:


Simplifying
x2 + 2x + -165 = 0

Reorder the terms:
-165 + 2x + x2 = 0

Solving
-165 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + 2x + 165 + x2 = 0 + 165

Reorder the terms:
-165 + 165 + 2x + x2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + 2x + x2 = 0 + 165
2x + x2 = 0 + 165

Combine like terms: 0 + 165 = 165
2x + x2 = 165

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 = 165 + 1

Reorder the terms:
1 + 2x + x2 = 165 + 1

Combine like terms: 165 + 1 = 166
1 + 2x + x2 = 166

Factor a perfect square on the left side:
(x + 1)(x + 1) = 166

Calculate the square root of the right side: 12.884098727

Break this problem into two subproblems by setting 
(x + 1) equal to 12.884098727 and -12.884098727.

Subproblem 1

x + 1 = 12.884098727 Simplifying x + 1 = 12.884098727 Reorder the terms: 1 + x = 12.884098727 Solving 1 + x = 12.884098727 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 = 12.884098727 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.884098727 + -1 x = 12.884098727 + -1 Combine like terms: 12.884098727 + -1 = 11.884098727 x = 11.884098727 Simplifying x = 11.884098727

Subproblem 2

x + 1 = -12.884098727 Simplifying x + 1 = -12.884098727 Reorder the terms: 1 + x = -12.884098727 Solving 1 + x = -12.884098727 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 = -12.884098727 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.884098727 + -1 x = -12.884098727 + -1 Combine like terms: -12.884098727 + -1 = -13.884098727 x = -13.884098727 Simplifying x = -13.884098727

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.884098727, -13.884098727}

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