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Simplifying x2 + 7ax + 12a2 = 0 Reorder the terms: 7ax + 12a2 + x2 = 0 Solving 7ax + 12a2 + x2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + x)(3a + x) = 0Subproblem 1
Set the factor '(4a + x)' equal to zero and attempt to solve: Simplifying 4a + x = 0 Solving 4a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. 4a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 4a + 0 = 0 + -1x 4a = 0 + -1x Remove the zero: 4a = -1x Divide each side by '4'. a = -0.25x Simplifying a = -0.25xSubproblem 2
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 = -0.3333333333xSolution
a = {-0.25x, -0.3333333333x}
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