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Simplifying 3x2 + 5ax + -2a2 = 0 Reorder the terms: 5ax + -2a2 + 3x2 = 0 Solving 5ax + -2a2 + 3x2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -1x)(a + -3x) = 0Subproblem 1
Set the factor '(-2a + -1x)' equal to zero and attempt to solve: Simplifying -2a + -1x = 0 Solving -2a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. -2a + -1x + x = 0 + x Combine like terms: -1x + x = 0 -2a + 0 = 0 + x -2a = 0 + x Remove the zero: -2a = x Divide each side by '-2'. a = -0.5x Simplifying a = -0.5xSubproblem 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 = 3xSolution
a = {-0.5x, 3x}
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