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Simplifying 10a2 = 32 + 32a Solving 10a2 = 32 + 32a Solving for variable 'a'. Reorder the terms: -32 + -32a + 10a2 = 32 + 32a + -32 + -32a Reorder the terms: -32 + -32a + 10a2 = 32 + -32 + 32a + -32a Combine like terms: 32 + -32 = 0 -32 + -32a + 10a2 = 0 + 32a + -32a -32 + -32a + 10a2 = 32a + -32a Combine like terms: 32a + -32a = 0 -32 + -32a + 10a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -16a + 5a2) = 0 Factor a trinomial. 2((-4 + -5a)(4 + -1a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve: Simplifying -4 + -5a = 0 Solving -4 + -5a = 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 + -5a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5a = 0 + 4 -5a = 0 + 4 Combine like terms: 0 + 4 = 4 -5a = 4 Divide each side by '-5'. a = -0.8 Simplifying a = -0.8Subproblem 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 = {-0.8, 4}
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