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Simplifying 12a2 + -20 = 22a Reorder the terms: -20 + 12a2 = 22a Solving -20 + 12a2 = 22a Solving for variable 'a'. Reorder the terms: -20 + -22a + 12a2 = 22a + -22a Combine like terms: 22a + -22a = 0 -20 + -22a + 12a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -11a + 6a2) = 0 Factor a trinomial. 2((-2 + -3a)(5 + -2a)) = 0 Ignore the factor 2.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 + -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 = 2.5Solution
a = {-0.6666666667, 2.5}
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