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Simplifying 16a2 + 16a = 10a2 + 11a + 39 Reorder the terms: 16a + 16a2 = 10a2 + 11a + 39 Reorder the terms: 16a + 16a2 = 39 + 11a + 10a2 Solving 16a + 16a2 = 39 + 11a + 10a2 Solving for variable 'a'. Reorder the terms: -39 + 16a + -11a + 16a2 + -10a2 = 39 + 11a + 10a2 + -39 + -11a + -10a2 Combine like terms: 16a + -11a = 5a -39 + 5a + 16a2 + -10a2 = 39 + 11a + 10a2 + -39 + -11a + -10a2 Combine like terms: 16a2 + -10a2 = 6a2 -39 + 5a + 6a2 = 39 + 11a + 10a2 + -39 + -11a + -10a2 Reorder the terms: -39 + 5a + 6a2 = 39 + -39 + 11a + -11a + 10a2 + -10a2 Combine like terms: 39 + -39 = 0 -39 + 5a + 6a2 = 0 + 11a + -11a + 10a2 + -10a2 -39 + 5a + 6a2 = 11a + -11a + 10a2 + -10a2 Combine like terms: 11a + -11a = 0 -39 + 5a + 6a2 = 0 + 10a2 + -10a2 -39 + 5a + 6a2 = 10a2 + -10a2 Combine like terms: 10a2 + -10a2 = 0 -39 + 5a + 6a2 = 0 Factor a trinomial. (-3 + -1a)(13 + -6a) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(13 + -6a)' equal to zero and attempt to solve: Simplifying 13 + -6a = 0 Solving 13 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -6a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -6a = 0 + -13 -6a = 0 + -13 Combine like terms: 0 + -13 = -13 -6a = -13 Divide each side by '-6'. a = 2.166666667 Simplifying a = 2.166666667Solution
a = {-3, 2.166666667}
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