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Simplifying 12a2 + 30a + 5 + 2a = 0 Reorder the terms: 5 + 30a + 2a + 12a2 = 0 Combine like terms: 30a + 2a = 32a 5 + 32a + 12a2 = 0 Solving 5 + 32a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + 2a)(1 + 6a) = 0Subproblem 1
Set the factor '(5 + 2a)' equal to zero and attempt to solve: Simplifying 5 + 2a = 0 Solving 5 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2a = 0 + -5 2a = 0 + -5 Combine like terms: 0 + -5 = -5 2a = -5 Divide each side by '2'. a = -2.5 Simplifying a = -2.5Subproblem 2
Set the factor '(1 + 6a)' equal to zero and attempt to solve: Simplifying 1 + 6a = 0 Solving 1 + 6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6a = 0 + -1 6a = 0 + -1 Combine like terms: 0 + -1 = -1 6a = -1 Divide each side by '6'. a = -0.1666666667 Simplifying a = -0.1666666667Solution
a = {-2.5, -0.1666666667}
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