z^2+zw+w^2=0

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Solution for z^2+zw+w^2=0 equation: 


Simplifying
z2 + zw + w2 = 0

Reorder the terms:
wz + w2 + z2 = 0

Solving
wz + w2 + z2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-1z2' to each side of the equation.
wz + w2 + z2 + -1z2 = 0 + -1z2

Combine like terms: z2 + -1z2 = 0
wz + w2 + 0 = 0 + -1z2
wz + w2 = 0 + -1z2
Remove the zero:
wz + w2 = -1z2

The w term is wz.  Take half its coefficient (0.5z).
Square it (0.25z2) and add it to both sides.

Add '0.25z2' to each side of the equation.
wz + w2 + 0.25z2 = -1z2 + 0.25z2

Combine like terms: -1z2 + 0.25z2 = -0.75z2
wz + w2 + 0.25z2 = -0.75z2

Factor a perfect square on the left side:
(w + 0.5z)(w + 0.5z) = -0.75z2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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