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Simplifying x2 + 4ax + 3a2 + 0 = 0 Reorder the terms: 0 + 4ax + 3a2 + x2 = 0 Remove the zero: 4ax + 3a2 + x2 = 0 Solving 4ax + 3a2 + x2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + x)(a + x) = 0Subproblem 1
Set the factor '(3a + x)' equal to zero and attempt to solve: Simplifying 3a + x = 0 Solving 3a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. 3a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 3a + 0 = 0 + -1x 3a = 0 + -1x Remove the zero: 3a = -1x 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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