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Simplifying 2x2 + 2ax + -12a2 = 0 Reorder the terms: 2ax + -12a2 + 2x2 = 0 Solving 2ax + -12a2 + 2x2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(ax + -6a2 + x2) = 0 Factor a trinomial. 2((-3a + -1x)(2a + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3a + -1x)' equal to zero and attempt to solve: Simplifying -3a + -1x = 0 Solving -3a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. -3a + -1x + x = 0 + x Combine like terms: -1x + x = 0 -3a + 0 = 0 + x -3a = 0 + x Remove the zero: -3a = x Divide each side by '-3'. a = -0.3333333333x Simplifying a = -0.3333333333xSubproblem 2
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 = 0.5xSolution
a = {-0.3333333333x, 0.5x}
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