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Simplifying 6a2 + 13a = 8 Reorder the terms: 13a + 6a2 = 8 Solving 13a + 6a2 = 8 Solving for variable 'a'. Reorder the terms: -8 + 13a + 6a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 13a + 6a2 = 0 Factor a trinomial. (-8 + -3a)(1 + -2a) = 0Subproblem 1
Set the factor '(-8 + -3a)' equal to zero and attempt to solve: Simplifying -8 + -3a = 0 Solving -8 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3a = 0 + 8 -3a = 0 + 8 Combine like terms: 0 + 8 = 8 -3a = 8 Divide each side by '-3'. a = -2.666666667 Simplifying a = -2.666666667Subproblem 2
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 = 0.5Solution
a = {-2.666666667, 0.5}
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