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Simplifying a(2a + 1) = 3 Reorder the terms: a(1 + 2a) = 3 (1 * a + 2a * a) = 3 (1a + 2a2) = 3 Solving 1a + 2a2 = 3 Solving for variable 'a'. Reorder the terms: -3 + 1a + 2a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 1a + 2a2 = 0 Factor a trinomial. (-3 + -2a)(1 + -1a) = 0Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {-1.5, 1}
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