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Simplifying 2a2 = 5a + 18 Reorder the terms: 2a2 = 18 + 5a Solving 2a2 = 18 + 5a Solving for variable 'a'. Reorder the terms: -18 + -5a + 2a2 = 18 + 5a + -18 + -5a Reorder the terms: -18 + -5a + 2a2 = 18 + -18 + 5a + -5a Combine like terms: 18 + -18 = 0 -18 + -5a + 2a2 = 0 + 5a + -5a -18 + -5a + 2a2 = 5a + -5a Combine like terms: 5a + -5a = 0 -18 + -5a + 2a2 = 0 Factor a trinomial. (-2 + -1a)(9 + -2a) = 0Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2Subproblem 2
Set the factor '(9 + -2a)' equal to zero and attempt to solve: Simplifying 9 + -2a = 0 Solving 9 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2a = 0 + -9 -2a = 0 + -9 Combine like terms: 0 + -9 = -9 -2a = -9 Divide each side by '-2'. a = 4.5 Simplifying a = 4.5Solution
a = {-2, 4.5}
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