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Simplifying 5a2 = 11a + 12 Reorder the terms: 5a2 = 12 + 11a Solving 5a2 = 12 + 11a Solving for variable 'a'. Reorder the terms: -12 + -11a + 5a2 = 12 + 11a + -12 + -11a Reorder the terms: -12 + -11a + 5a2 = 12 + -12 + 11a + -11a Combine like terms: 12 + -12 = 0 -12 + -11a + 5a2 = 0 + 11a + -11a -12 + -11a + 5a2 = 11a + -11a Combine like terms: 11a + -11a = 0 -12 + -11a + 5a2 = 0 Factor a trinomial. (-4 + -5a)(3 + -1a) = 0Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve: Simplifying -4 + -5a = 0 Solving -4 + -5a = 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 + -5a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5a = 0 + 4 -5a = 0 + 4 Combine like terms: 0 + 4 = 4 -5a = 4 Divide each side by '-5'. a = -0.8 Simplifying a = -0.8Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-0.8, 3}
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