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Simplifying 30a2 = 18 + 33a Solving 30a2 = 18 + 33a Solving for variable 'a'. Reorder the terms: -18 + -33a + 30a2 = 18 + 33a + -18 + -33a Reorder the terms: -18 + -33a + 30a2 = 18 + -18 + 33a + -33a Combine like terms: 18 + -18 = 0 -18 + -33a + 30a2 = 0 + 33a + -33a -18 + -33a + 30a2 = 33a + -33a Combine like terms: 33a + -33a = 0 -18 + -33a + 30a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -11a + 10a2) = 0 Factor a trinomial. 3((-2 + -5a)(3 + -2a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -5a)' equal to zero and attempt to solve: Simplifying -2 + -5a = 0 Solving -2 + -5a = 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 + -5a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5a = 0 + 2 -5a = 0 + 2 Combine like terms: 0 + 2 = 2 -5a = 2 Divide each side by '-5'. a = -0.4 Simplifying a = -0.4Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-0.4, 1.5}
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