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Simplifying 3a2 = 68 + 5a Solving 3a2 = 68 + 5a Solving for variable 'a'. Reorder the terms: -68 + -5a + 3a2 = 68 + 5a + -68 + -5a Reorder the terms: -68 + -5a + 3a2 = 68 + -68 + 5a + -5a Combine like terms: 68 + -68 = 0 -68 + -5a + 3a2 = 0 + 5a + -5a -68 + -5a + 3a2 = 5a + -5a Combine like terms: 5a + -5a = 0 -68 + -5a + 3a2 = 0 Factor a trinomial. (-4 + -1a)(17 + -3a) = 0Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 2
Set the factor '(17 + -3a)' equal to zero and attempt to solve: Simplifying 17 + -3a = 0 Solving 17 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -3a = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3a = 0 + -17 -3a = 0 + -17 Combine like terms: 0 + -17 = -17 -3a = -17 Divide each side by '-3'. a = 5.666666667 Simplifying a = 5.666666667Solution
a = {-4, 5.666666667}
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