x^2+2x-162=0

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Solution for x^2+2x-162=0 equation:


Simplifying
x2 + 2x + -162 = 0

Reorder the terms:
-162 + 2x + x2 = 0

Solving
-162 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '162' to each side of the equation.
-162 + 2x + 162 + x2 = 0 + 162

Reorder the terms:
-162 + 162 + 2x + x2 = 0 + 162

Combine like terms: -162 + 162 = 0
0 + 2x + x2 = 0 + 162
2x + x2 = 0 + 162

Combine like terms: 0 + 162 = 162
2x + x2 = 162

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 = 162 + 1

Reorder the terms:
1 + 2x + x2 = 162 + 1

Combine like terms: 162 + 1 = 163
1 + 2x + x2 = 163

Factor a perfect square on the left side:
(x + 1)(x + 1) = 163

Calculate the square root of the right side: 12.767145335

Break this problem into two subproblems by setting 
(x + 1) equal to 12.767145335 and -12.767145335.

Subproblem 1

x + 1 = 12.767145335 Simplifying x + 1 = 12.767145335 Reorder the terms: 1 + x = 12.767145335 Solving 1 + x = 12.767145335 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 = 12.767145335 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.767145335 + -1 x = 12.767145335 + -1 Combine like terms: 12.767145335 + -1 = 11.767145335 x = 11.767145335 Simplifying x = 11.767145335

Subproblem 2

x + 1 = -12.767145335 Simplifying x + 1 = -12.767145335 Reorder the terms: 1 + x = -12.767145335 Solving 1 + x = -12.767145335 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 = -12.767145335 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.767145335 + -1 x = -12.767145335 + -1 Combine like terms: -12.767145335 + -1 = -13.767145335 x = -13.767145335 Simplifying x = -13.767145335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.767145335, -13.767145335}

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