x^2+2x+k^2=0

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


Simplifying
x2 + 2x + k2 = 0

Reorder the terms:
k2 + 2x + x2 = 0

Solving
k2 + 2x + x2 = 0

Solving for variable 'k'.

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

Add '-2x' to each side of the equation.
k2 + 2x + -2x + x2 = 0 + -2x

Combine like terms: 2x + -2x = 0
k2 + 0 + x2 = 0 + -2x
k2 + x2 = 0 + -2x
Remove the zero:
k2 + x2 = -2x

Add '-1x2' to each side of the equation.
k2 + x2 + -1x2 = -2x + -1x2

Combine like terms: x2 + -1x2 = 0
k2 + 0 = -2x + -1x2
k2 = -2x + -1x2

Simplifying
k2 = -2x + -1x2

Reorder the terms:
k2 + 2x + x2 = -2x + 2x + -1x2 + x2

Combine like terms: -2x + 2x = 0
k2 + 2x + x2 = 0 + -1x2 + x2
k2 + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
k2 + 2x + x2 = 0

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


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

Simplifying
k + x = 0

Solving
k + x = 0

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

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

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

Simplifying
k = -1x

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

Simplifying
k + x = 0

Solving
k + x = 0

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

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

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

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

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