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Simplifying (3a + -1)(3a + -1) + -6a + 2 = 0 Reorder the terms: (-1 + 3a)(3a + -1) + -6a + 2 = 0 Reorder the terms: (-1 + 3a)(-1 + 3a) + -6a + 2 = 0 Multiply (-1 + 3a) * (-1 + 3a) (-1(-1 + 3a) + 3a * (-1 + 3a)) + -6a + 2 = 0 ((-1 * -1 + 3a * -1) + 3a * (-1 + 3a)) + -6a + 2 = 0 ((1 + -3a) + 3a * (-1 + 3a)) + -6a + 2 = 0 (1 + -3a + (-1 * 3a + 3a * 3a)) + -6a + 2 = 0 (1 + -3a + (-3a + 9a2)) + -6a + 2 = 0 Combine like terms: -3a + -3a = -6a (1 + -6a + 9a2) + -6a + 2 = 0 Reorder the terms: 1 + 2 + -6a + -6a + 9a2 = 0 Combine like terms: 1 + 2 = 3 3 + -6a + -6a + 9a2 = 0 Combine like terms: -6a + -6a = -12a 3 + -12a + 9a2 = 0 Solving 3 + -12a + 9a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -4a + 3a2) = 0 Factor a trinomial. 3((1 + -3a)(1 + -1a)) = 0 Ignore the factor 3.Subproblem 1
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 = 0.3333333333Subproblem 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 = {0.3333333333, 1}
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