3x^2+2ax-a^2=0

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Solution for 3x^2+2ax-a^2=0 equation:


Simplifying
3x2 + 2ax + -1a2 = 0

Reorder the terms:
2ax + -1a2 + 3x2 = 0

Solving
2ax + -1a2 + 3x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1a + -1x)(a + -3x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(a + -3x)' equal to zero and attempt to solve: Simplifying a + -3x = 0 Solving a + -3x = 0 Move all terms containing a to the left, all other terms to the right. Add '3x' to each side of the equation. a + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 a + 0 = 0 + 3x a = 0 + 3x Remove the zero: a = 3x Simplifying a = 3x

Solution

a = {-1x, 3x}

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