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Simplifying 5a2 + -2a + -8 + -1a2 + -6a + 3 = 0 Reorder the terms: -8 + 3 + -2a + -6a + 5a2 + -1a2 = 0 Combine like terms: -8 + 3 = -5 -5 + -2a + -6a + 5a2 + -1a2 = 0 Combine like terms: -2a + -6a = -8a -5 + -8a + 5a2 + -1a2 = 0 Combine like terms: 5a2 + -1a2 = 4a2 -5 + -8a + 4a2 = 0 Solving -5 + -8a + 4a2 = 0 Solving for variable 'a'. Factor a trinomial. (-1 + -2a)(5 + -2a) = 0Subproblem 1
Set the factor '(-1 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 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 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5Subproblem 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 = {-0.5, 2.5}
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