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Simplifying 10a2 + -58a + 64 = -3a + 4 Reorder the terms: 64 + -58a + 10a2 = -3a + 4 Reorder the terms: 64 + -58a + 10a2 = 4 + -3a Solving 64 + -58a + 10a2 = 4 + -3a Solving for variable 'a'. Reorder the terms: 64 + -4 + -58a + 3a + 10a2 = 4 + -3a + -4 + 3a Combine like terms: 64 + -4 = 60 60 + -58a + 3a + 10a2 = 4 + -3a + -4 + 3a Combine like terms: -58a + 3a = -55a 60 + -55a + 10a2 = 4 + -3a + -4 + 3a Reorder the terms: 60 + -55a + 10a2 = 4 + -4 + -3a + 3a Combine like terms: 4 + -4 = 0 60 + -55a + 10a2 = 0 + -3a + 3a 60 + -55a + 10a2 = -3a + 3a Combine like terms: -3a + 3a = 0 60 + -55a + 10a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(12 + -11a + 2a2) = 0 Factor a trinomial. 5((3 + -2a)(4 + -1a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Solution
a = {1.5, 4}
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