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Simplifying 15a2 = -66a + 45 Reorder the terms: 15a2 = 45 + -66a Solving 15a2 = 45 + -66a Solving for variable 'a'. Reorder the terms: -45 + 66a + 15a2 = 45 + -66a + -45 + 66a Reorder the terms: -45 + 66a + 15a2 = 45 + -45 + -66a + 66a Combine like terms: 45 + -45 = 0 -45 + 66a + 15a2 = 0 + -66a + 66a -45 + 66a + 15a2 = -66a + 66a Combine like terms: -66a + 66a = 0 -45 + 66a + 15a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 22a + 5a2) = 0 Factor a trinomial. 3((-5 + -1a)(3 + -5a)) = 0 Ignore the factor 3.Subproblem 1
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 = -5Subproblem 2
Set the factor '(3 + -5a)' equal to zero and attempt to solve: Simplifying 3 + -5a = 0 Solving 3 + -5a = 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 + -5a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5a = 0 + -3 -5a = 0 + -3 Combine like terms: 0 + -3 = -3 -5a = -3 Divide each side by '-5'. a = 0.6 Simplifying a = 0.6Solution
a = {-5, 0.6}
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