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Simplifying 3a2 + 5a + 8 = 500 Reorder the terms: 8 + 5a + 3a2 = 500 Solving 8 + 5a + 3a2 = 500 Solving for variable 'a'. Reorder the terms: 8 + -500 + 5a + 3a2 = 500 + -500 Combine like terms: 8 + -500 = -492 -492 + 5a + 3a2 = 500 + -500 Combine like terms: 500 + -500 = 0 -492 + 5a + 3a2 = 0 Factor a trinomial. (-41 + -3a)(12 + -1a) = 0Subproblem 1
Set the factor '(-41 + -3a)' equal to zero and attempt to solve: Simplifying -41 + -3a = 0 Solving -41 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + -3a = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -3a = 0 + 41 -3a = 0 + 41 Combine like terms: 0 + 41 = 41 -3a = 41 Divide each side by '-3'. a = -13.66666667 Simplifying a = -13.66666667Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve: Simplifying 12 + -1a = 0 Solving 12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1a = 0 + -12 -1a = 0 + -12 Combine like terms: 0 + -12 = -12 -1a = -12 Divide each side by '-1'. a = 12 Simplifying a = 12Solution
a = {-13.66666667, 12}
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