z^2+2az+a^2=0

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Solution for z^2+2az+a^2=0 equation:


Simplifying
z2 + 2az + a2 = 0

Reorder the terms:
2az + a2 + z2 = 0

Solving
2az + a2 + z2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + z)(a + z) = 0

Subproblem 1

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

Subproblem 2

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

Solution

a = {-1z, -1z}

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