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Simplifying 20a2 + -11a = 3 Reorder the terms: -11a + 20a2 = 3 Solving -11a + 20a2 = 3 Solving for variable 'a'. Reorder the terms: -3 + -11a + 20a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -11a + 20a2 = 0 Factor a trinomial. (-1 + -5a)(3 + -4a) = 0Subproblem 1
Set the factor '(-1 + -5a)' equal to zero and attempt to solve: Simplifying -1 + -5a = 0 Solving -1 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5a = 0 + 1 -5a = 0 + 1 Combine like terms: 0 + 1 = 1 -5a = 1 Divide each side by '-5'. a = -0.2 Simplifying a = -0.2Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 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 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Solution
a = {-0.2, 0.75}
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