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Simplifying 9a2 + -6a + 1 = 169 Reorder the terms: 1 + -6a + 9a2 = 169 Solving 1 + -6a + 9a2 = 169 Solving for variable 'a'. Reorder the terms: 1 + -169 + -6a + 9a2 = 169 + -169 Combine like terms: 1 + -169 = -168 -168 + -6a + 9a2 = 169 + -169 Combine like terms: 169 + -169 = 0 -168 + -6a + 9a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-56 + -2a + 3a2) = 0 Factor a trinomial. 3((-4 + -1a)(14 + -3a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 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 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 2
Set the factor '(14 + -3a)' equal to zero and attempt to solve: Simplifying 14 + -3a = 0 Solving 14 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -3a = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -3a = 0 + -14 -3a = 0 + -14 Combine like terms: 0 + -14 = -14 -3a = -14 Divide each side by '-3'. a = 4.666666667 Simplifying a = 4.666666667Solution
a = {-4, 4.666666667}
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