x+2x^2+1=-1-x

Solution for x+2x^2+1=-1-x equation:

Simplifying
x + 2x2 + 1 = -1 + -1x

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

Solving
1 + x + 2x2 = -1 + -1x

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Simplifying
1 + x + x2 = 0

Solving
1 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + x + x2 = 0 + -1

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

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

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 = -1 + 0.25

Reorder the terms:
0.25 + x + x2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + x + x2 = -0.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.75

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.