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Simplifying 16a2 = 60 + 68a Solving 16a2 = 60 + 68a Solving for variable 'a'. Reorder the terms: -60 + -68a + 16a2 = 60 + 68a + -60 + -68a Reorder the terms: -60 + -68a + 16a2 = 60 + -60 + 68a + -68a Combine like terms: 60 + -60 = 0 -60 + -68a + 16a2 = 0 + 68a + -68a -60 + -68a + 16a2 = 68a + -68a Combine like terms: 68a + -68a = 0 -60 + -68a + 16a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -17a + 4a2) = 0 Factor a trinomial. 4((-3 + -4a)(5 + -1a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve: Simplifying -3 + -4a = 0 Solving -3 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4a = 0 + 3 -4a = 0 + 3 Combine like terms: 0 + 3 = 3 -4a = 3 Divide each side by '-4'. a = -0.75 Simplifying a = -0.75Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 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 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {-0.75, 5}
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