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Simplifying a + 3 = (a + -2) * 2a + -4 Reorder the terms: 3 + a = (a + -2) * 2a + -4 Reorder the terms: 3 + a = (-2 + a) * 2a + -4 Reorder the terms for easier multiplication: 3 + a = 2a(-2 + a) + -4 3 + a = (-2 * 2a + a * 2a) + -4 3 + a = (-4a + 2a2) + -4 Reorder the terms: 3 + a = -4 + -4a + 2a2 Solving 3 + a = -4 + -4a + 2a2 Solving for variable 'a'. Reorder the terms: 3 + 4 + a + 4a + -2a2 = -4 + -4a + 2a2 + 4 + 4a + -2a2 Combine like terms: 3 + 4 = 7 7 + a + 4a + -2a2 = -4 + -4a + 2a2 + 4 + 4a + -2a2 Combine like terms: a + 4a = 5a 7 + 5a + -2a2 = -4 + -4a + 2a2 + 4 + 4a + -2a2 Reorder the terms: 7 + 5a + -2a2 = -4 + 4 + -4a + 4a + 2a2 + -2a2 Combine like terms: -4 + 4 = 0 7 + 5a + -2a2 = 0 + -4a + 4a + 2a2 + -2a2 7 + 5a + -2a2 = -4a + 4a + 2a2 + -2a2 Combine like terms: -4a + 4a = 0 7 + 5a + -2a2 = 0 + 2a2 + -2a2 7 + 5a + -2a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 7 + 5a + -2a2 = 0 Factor a trinomial. (7 + -2a)(1 + a) = 0Subproblem 1
Set the factor '(7 + -2a)' equal to zero and attempt to solve: Simplifying 7 + -2a = 0 Solving 7 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2a = 0 + -7 -2a = 0 + -7 Combine like terms: 0 + -7 = -7 -2a = -7 Divide each side by '-2'. a = 3.5 Simplifying a = 3.5Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {3.5, -1}
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