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Simplifying 230 = 2a2 + 3a Reorder the terms: 230 = 3a + 2a2 Solving 230 = 3a + 2a2 Solving for variable 'a'. Reorder the terms: 230 + -3a + -2a2 = 3a + -3a + 2a2 + -2a2 Combine like terms: 3a + -3a = 0 230 + -3a + -2a2 = 0 + 2a2 + -2a2 230 + -3a + -2a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 230 + -3a + -2a2 = 0 Factor a trinomial. (10 + -1a)(23 + 2a) = 0Subproblem 1
Set the factor '(10 + -1a)' equal to zero and attempt to solve: Simplifying 10 + -1a = 0 Solving 10 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1a = 0 + -10 -1a = 0 + -10 Combine like terms: 0 + -10 = -10 -1a = -10 Divide each side by '-1'. a = 10 Simplifying a = 10Subproblem 2
Set the factor '(23 + 2a)' equal to zero and attempt to solve: Simplifying 23 + 2a = 0 Solving 23 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 2a = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 2a = 0 + -23 2a = 0 + -23 Combine like terms: 0 + -23 = -23 2a = -23 Divide each side by '2'. a = -11.5 Simplifying a = -11.5Solution
a = {10, -11.5}
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