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Simplifying 10 = 4a2 + 18a Reorder the terms: 10 = 18a + 4a2 Solving 10 = 18a + 4a2 Solving for variable 'a'. Reorder the terms: 10 + -18a + -4a2 = 18a + -18a + 4a2 + -4a2 Combine like terms: 18a + -18a = 0 10 + -18a + -4a2 = 0 + 4a2 + -4a2 10 + -18a + -4a2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 10 + -18a + -4a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -9a + -2a2) = 0 Factor a trinomial. 2((1 + -2a)(5 + a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Subproblem 2
Set the factor '(5 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5Solution
a = {0.5, -5}
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