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Simplifying 9a2 = 7 + 18a Solving 9a2 = 7 + 18a Solving for variable 'a'. Reorder the terms: -7 + -18a + 9a2 = 7 + 18a + -7 + -18a Reorder the terms: -7 + -18a + 9a2 = 7 + -7 + 18a + -18a Combine like terms: 7 + -7 = 0 -7 + -18a + 9a2 = 0 + 18a + -18a -7 + -18a + 9a2 = 18a + -18a Combine like terms: 18a + -18a = 0 -7 + -18a + 9a2 = 0 Factor a trinomial. (-1 + -3a)(7 + -3a) = 0Subproblem 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 '(7 + -3a)' equal to zero and attempt to solve: Simplifying 7 + -3a = 0 Solving 7 + -3a = 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 + -3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3a = 0 + -7 -3a = 0 + -7 Combine like terms: 0 + -7 = -7 -3a = -7 Divide each side by '-3'. a = 2.333333333 Simplifying a = 2.333333333Solution
a = {-0.3333333333, 2.333333333}
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