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Simplifying 6x2 + 7ax + 2a2 = 0 Reorder the terms: 7ax + 2a2 + 6x2 = 0 Solving 7ax + 2a2 + 6x2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + 3x)(a + 2x) = 0Subproblem 1
Set the factor '(2a + 3x)' equal to zero and attempt to solve: Simplifying 2a + 3x = 0 Solving 2a + 3x = 0 Move all terms containing a to the left, all other terms to the right. Add '-3x' to each side of the equation. 2a + 3x + -3x = 0 + -3x Combine like terms: 3x + -3x = 0 2a + 0 = 0 + -3x 2a = 0 + -3x Remove the zero: 2a = -3x Divide each side by '2'. a = -1.5x Simplifying a = -1.5xSubproblem 2
Set the factor '(a + 2x)' equal to zero and attempt to solve: Simplifying a + 2x = 0 Solving a + 2x = 0 Move all terms containing a to the left, all other terms to the right. Add '-2x' to each side of the equation. a + 2x + -2x = 0 + -2x Combine like terms: 2x + -2x = 0 a + 0 = 0 + -2x a = 0 + -2x Remove the zero: a = -2x Simplifying a = -2xSolution
a = {-1.5x, -2x}
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