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Simplifying 18a2 + -14 + -3a = 42a + -42 Reorder the terms: -14 + -3a + 18a2 = 42a + -42 Reorder the terms: -14 + -3a + 18a2 = -42 + 42a Solving -14 + -3a + 18a2 = -42 + 42a Solving for variable 'a'. Reorder the terms: -14 + 42 + -3a + -42a + 18a2 = -42 + 42a + 42 + -42a Combine like terms: -14 + 42 = 28 28 + -3a + -42a + 18a2 = -42 + 42a + 42 + -42a Combine like terms: -3a + -42a = -45a 28 + -45a + 18a2 = -42 + 42a + 42 + -42a Reorder the terms: 28 + -45a + 18a2 = -42 + 42 + 42a + -42a Combine like terms: -42 + 42 = 0 28 + -45a + 18a2 = 0 + 42a + -42a 28 + -45a + 18a2 = 42a + -42a Combine like terms: 42a + -42a = 0 28 + -45a + 18a2 = 0 Factor a trinomial. (7 + -6a)(4 + -3a) = 0Subproblem 1
Set the factor '(7 + -6a)' equal to zero and attempt to solve: Simplifying 7 + -6a = 0 Solving 7 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6a = 0 + -7 -6a = 0 + -7 Combine like terms: 0 + -7 = -7 -6a = -7 Divide each side by '-6'. a = 1.166666667 Simplifying a = 1.166666667Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {1.166666667, 1.333333333}
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