x=x^2+2x+2

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


Simplifying
x = x2 + 2x + 2

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

Solving
x = 2 + 2x + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Ignore the factor -1.

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

Simplifying
2 + x + x2 = 0

Solving
2 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -2 + 0.25

Reorder the terms:
0.25 + x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + x + x2 = -1.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.75

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.

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