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Simplifying 9a2 = 30 + 39a Solving 9a2 = 30 + 39a Solving for variable 'a'. Reorder the terms: -30 + -39a + 9a2 = 30 + 39a + -30 + -39a Reorder the terms: -30 + -39a + 9a2 = 30 + -30 + 39a + -39a Combine like terms: 30 + -30 = 0 -30 + -39a + 9a2 = 0 + 39a + -39a -30 + -39a + 9a2 = 39a + -39a Combine like terms: 39a + -39a = 0 -30 + -39a + 9a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -13a + 3a2) = 0 Factor a trinomial. 3((-2 + -3a)(5 + -1a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -3a)' equal to zero and attempt to solve: Simplifying -2 + -3a = 0 Solving -2 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3a = 0 + 2 -3a = 0 + 2 Combine like terms: 0 + 2 = 2 -3a = 2 Divide each side by '-3'. a = -0.6666666667 Simplifying a = -0.6666666667Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 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 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {-0.6666666667, 5}
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