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Simplifying 4a2 = 56 + 20a Solving 4a2 = 56 + 20a Solving for variable 'a'. Reorder the terms: -56 + -20a + 4a2 = 56 + 20a + -56 + -20a Reorder the terms: -56 + -20a + 4a2 = 56 + -56 + 20a + -20a Combine like terms: 56 + -56 = 0 -56 + -20a + 4a2 = 0 + 20a + -20a -56 + -20a + 4a2 = 20a + -20a Combine like terms: 20a + -20a = 0 -56 + -20a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + -5a + a2) = 0 Factor a trinomial. 4((-2 + -1a)(7 + -1a)) = 0 Ignore the factor 4.Subproblem 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 '(7 + -1a)' equal to zero and attempt to solve: Simplifying 7 + -1a = 0 Solving 7 + -1a = 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 + -1a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1a = 0 + -7 -1a = 0 + -7 Combine like terms: 0 + -7 = -7 -1a = -7 Divide each side by '-1'. a = 7 Simplifying a = 7Solution
a = {-2, 7}
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