2x^2+2x-342=0

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Solution for 2x^2+2x-342=0 equation: 


Simplifying
2x2 + 2x + -342 = 0

Reorder the terms:
-342 + 2x + 2x2 = 0

Solving
-342 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-171 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-171 + x + x2)' equal to zero and attempt to solve:

Simplifying
-171 + x + x2 = 0

Solving
-171 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '171' to each side of the equation.
-171 + x + 171 + x2 = 0 + 171

Reorder the terms:
-171 + 171 + x + x2 = 0 + 171

Combine like terms: -171 + 171 = 0
0 + x + x2 = 0 + 171
x + x2 = 0 + 171

Combine like terms: 0 + 171 = 171
x + x2 = 171

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 = 171 + 0.25

Reorder the terms:
0.25 + x + x2 = 171 + 0.25

Combine like terms: 171 + 0.25 = 171.25
0.25 + x + x2 = 171.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 171.25

Calculate the square root of the right side: 13.086252328

Break this problem into two subproblems by setting 
(x + 0.5) equal to 13.086252328 and -13.086252328.


Subproblem 1
x + 0.5 = 13.086252328

Simplifying
x + 0.5 = 13.086252328

Reorder the terms:
0.5 + x = 13.086252328

Solving
0.5 + x = 13.086252328

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 = 13.086252328 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 13.086252328 + -0.5
x = 13.086252328 + -0.5

Combine like terms: 13.086252328 + -0.5 = 12.586252328
x = 12.586252328

Simplifying
x = 12.586252328


Subproblem 2
x + 0.5 = -13.086252328

Simplifying
x + 0.5 = -13.086252328

Reorder the terms:
0.5 + x = -13.086252328

Solving
0.5 + x = -13.086252328

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 = -13.086252328 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -13.086252328 + -0.5
x = -13.086252328 + -0.5

Combine like terms: -13.086252328 + -0.5 = -13.586252328
x = -13.586252328

Simplifying
x = -13.586252328


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.586252328, -13.586252328}
Solution
x = {12.586252328, -13.586252328}

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