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Simplifying 9a(a + 1) = 4 Reorder the terms: 9a(1 + a) = 4 (1 * 9a + a * 9a) = 4 (9a + 9a2) = 4 Solving 9a + 9a2 = 4 Solving for variable 'a'. Reorder the terms: -4 + 9a + 9a2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 9a + 9a2 = 0 Factor a trinomial. (-4 + -3a)(1 + -3a) = 0Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve: Simplifying -4 + -3a = 0 Solving -4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3a = 0 + 4 -3a = 0 + 4 Combine like terms: 0 + 4 = 4 -3a = 4 Divide each side by '-3'. a = -1.333333333 Simplifying a = -1.333333333Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 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 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Solution
a = {-1.333333333, 0.3333333333}
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