0=x^2+2x-167

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Solution for 0=x^2+2x-167 equation:


Simplifying
0 = x2 + 2x + -167

Reorder the terms:
0 = -167 + 2x + x2

Solving
0 = -167 + 2x + x2

Solving for variable 'x'.

Combine like terms: 0 + 167 = 167
167 + -2x + -1x2 = -167 + 2x + x2 + 167 + -2x + -1x2

Reorder the terms:
167 + -2x + -1x2 = -167 + 167 + 2x + -2x + x2 + -1x2

Combine like terms: -167 + 167 = 0
167 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
167 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
167 + -2x + -1x2 = 0 + x2 + -1x2
167 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
167 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-167 + 2x + x2 = 0

Move the constant term to the right:

Add '167' to each side of the equation.
-167 + 2x + 167 + x2 = 0 + 167

Reorder the terms:
-167 + 167 + 2x + x2 = 0 + 167

Combine like terms: -167 + 167 = 0
0 + 2x + x2 = 0 + 167
2x + x2 = 0 + 167

Combine like terms: 0 + 167 = 167
2x + x2 = 167

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 = 167 + 1

Reorder the terms:
1 + 2x + x2 = 167 + 1

Combine like terms: 167 + 1 = 168
1 + 2x + x2 = 168

Factor a perfect square on the left side:
(x + 1)(x + 1) = 168

Calculate the square root of the right side: 12.961481397

Break this problem into two subproblems by setting 
(x + 1) equal to 12.961481397 and -12.961481397.

Subproblem 1

x + 1 = 12.961481397 Simplifying x + 1 = 12.961481397 Reorder the terms: 1 + x = 12.961481397 Solving 1 + x = 12.961481397 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 = 12.961481397 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.961481397 + -1 x = 12.961481397 + -1 Combine like terms: 12.961481397 + -1 = 11.961481397 x = 11.961481397 Simplifying x = 11.961481397

Subproblem 2

x + 1 = -12.961481397 Simplifying x + 1 = -12.961481397 Reorder the terms: 1 + x = -12.961481397 Solving 1 + x = -12.961481397 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 = -12.961481397 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.961481397 + -1 x = -12.961481397 + -1 Combine like terms: -12.961481397 + -1 = -13.961481397 x = -13.961481397 Simplifying x = -13.961481397

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.961481397, -13.961481397}

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