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Simplifying 6a2 + 4ax + -2x2 = 0 Reorder the terms: 4ax + 6a2 + -2x2 = 0 Solving 4ax + 6a2 + -2x2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(2ax + 3a2 + -1x2) = 0 Factor a trinomial. 2((3a + -1x)(a + x)) = 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 '(a + x)' equal to zero and attempt to solve: Simplifying a + x = 0 Solving a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 a + 0 = 0 + -1x a = 0 + -1x Remove the zero: a = -1x Simplifying a = -1xSolution
a = {0.3333333333x, -1x}
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