x^2+2*x*y+y^2=0

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Solution for x^2+2*x*y+y^2=0 equation:


Simplifying
x2 + 2x * y + y2 = 0

Multiply x * y
x2 + 2xy + y2 = 0

Reorder the terms:
2xy + x2 + y2 = 0

Solving
2xy + x2 + y2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1y

Subproblem 2

Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1y

Solution

x = {-1y, -1y}

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