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