X^2+2x+x^2=0

Solution for X^2+2x+x^2=0 equation:

Simplifying
X2 + 2x + x2 = 0

Solving
X2 + 2x + x2 = 0

Solving for variable 'X'.

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

Add '-2x' to each side of the equation.
X2 + 2x + -2x + x2 = 0 + -2x

Combine like terms: 2x + -2x = 0
X2 + 0 + x2 = 0 + -2x
X2 + x2 = 0 + -2x
Remove the zero:
X2 + x2 = -2x

Add '-1x2' to each side of the equation.
X2 + x2 + -1x2 = -2x + -1x2

Combine like terms: x2 + -1x2 = 0
X2 + 0 = -2x + -1x2
X2 = -2x + -1x2

Simplifying
X2 = -2x + -1x2

Reorder the terms:
X2 + 2x + x2 = -2x + 2x + -1x2 + x2

Combine like terms: -2x + 2x = 0
X2 + 2x + x2 = 0 + -1x2 + x2
X2 + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
X2 + 2x + x2 = 0

Factor a trinomial.
(X + x)(X + x) = 0

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

Simplifying
X + x = 0

Solving
X + x = 0

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

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

Combine like terms: x + -1x = 0
X + 0 = 0 + -1x
X = 0 + -1x
Remove the zero:
X = -1x

Simplifying
X = -1x
Subproblem 2
Set the factor '(X + x)' equal to zero and attempt to solve:

Simplifying
X + x = 0

Solving
X + x = 0

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

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

Combine like terms: x + -1x = 0
X + 0 = 0 + -1x
X = 0 + -1x
Remove the zero:
X = -1x

Simplifying
X = -1x
Solution
X = {-1x, -1x}