4x^2+2=-2x

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Solution for 4x^2+2=-2x equation: 


Simplifying
4x2 + 2 = -2x

Reorder the terms:
2 + 4x2 = -2x

Solving
2 + 4x2 = -2x

Solving for variable 'x'.

Reorder the terms:
2 + 2x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
2 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + x + 2x2 = 0

Solving
1 + x + 2x2 = 0

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

Divide each side by '2'.
0.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.5x + x2 = 0 + -0.5
0.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.5x + x2 = -0.5

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.
0.5x + 0.25 + x2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.5x + x2 = -0.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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