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Simplifying 5a2 + -16a = 7a + -24 Reorder the terms: -16a + 5a2 = 7a + -24 Reorder the terms: -16a + 5a2 = -24 + 7a Solving -16a + 5a2 = -24 + 7a Solving for variable 'a'. Reorder the terms: 24 + -16a + -7a + 5a2 = -24 + 7a + 24 + -7a Combine like terms: -16a + -7a = -23a 24 + -23a + 5a2 = -24 + 7a + 24 + -7a Reorder the terms: 24 + -23a + 5a2 = -24 + 24 + 7a + -7a Combine like terms: -24 + 24 = 0 24 + -23a + 5a2 = 0 + 7a + -7a 24 + -23a + 5a2 = 7a + -7a Combine like terms: 7a + -7a = 0 24 + -23a + 5a2 = 0 Factor a trinomial. (8 + -5a)(3 + -1a) = 0Subproblem 1
Set the factor '(8 + -5a)' equal to zero and attempt to solve: Simplifying 8 + -5a = 0 Solving 8 + -5a = 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 + -5a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5a = 0 + -8 -5a = 0 + -8 Combine like terms: 0 + -8 = -8 -5a = -8 Divide each side by '-5'. a = 1.6 Simplifying a = 1.6Subproblem 2
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 = 3Solution
a = {1.6, 3}
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