2x^2+2x-168=0

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Solution for 2x^2+2x-168=0 equation: 


Simplifying
2x2 + 2x + -168 = 0

Reorder the terms:
-168 + 2x + 2x2 = 0

Solving
-168 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-84 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-84 + x + x2)' equal to zero and attempt to solve:

Simplifying
-84 + x + x2 = 0

Solving
-84 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + x + x2 = 0 + 84
x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
x + x2 = 84

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 84 + 0.25

Reorder the terms:
0.25 + x + x2 = 84 + 0.25

Combine like terms: 84 + 0.25 = 84.25
0.25 + x + x2 = 84.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.178779875 and -9.178779875.


Subproblem 1
x + 0.5 = 9.178779875

Simplifying
x + 0.5 = 9.178779875

Reorder the terms:
0.5 + x = 9.178779875

Solving
0.5 + x = 9.178779875

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 9.178779875 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 9.178779875 + -0.5
x = 9.178779875 + -0.5

Combine like terms: 9.178779875 + -0.5 = 8.678779875
x = 8.678779875

Simplifying
x = 8.678779875


Subproblem 2
x + 0.5 = -9.178779875

Simplifying
x + 0.5 = -9.178779875

Reorder the terms:
0.5 + x = -9.178779875

Solving
0.5 + x = -9.178779875

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -9.178779875 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -9.178779875 + -0.5
x = -9.178779875 + -0.5

Combine like terms: -9.178779875 + -0.5 = -9.678779875
x = -9.678779875

Simplifying
x = -9.678779875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.678779875, -9.678779875}
Solution
x = {8.678779875, -9.678779875}

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