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Simplifying (8a + -2)(2a + -8) = 0 Reorder the terms: (-2 + 8a)(2a + -8) = 0 Reorder the terms: (-2 + 8a)(-8 + 2a) = 0 Multiply (-2 + 8a) * (-8 + 2a) (-2(-8 + 2a) + 8a * (-8 + 2a)) = 0 ((-8 * -2 + 2a * -2) + 8a * (-8 + 2a)) = 0 ((16 + -4a) + 8a * (-8 + 2a)) = 0 (16 + -4a + (-8 * 8a + 2a * 8a)) = 0 (16 + -4a + (-64a + 16a2)) = 0 Combine like terms: -4a + -64a = -68a (16 + -68a + 16a2) = 0 Solving 16 + -68a + 16a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -17a + 4a2) = 0 Factor a trinomial. 4((1 + -4a)(4 + -1a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -4a)' equal to zero and attempt to solve: Simplifying 1 + -4a = 0 Solving 1 + -4a = 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 + -4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4a = 0 + -1 -4a = 0 + -1 Combine like terms: 0 + -1 = -1 -4a = -1 Divide each side by '-4'. a = 0.25 Simplifying a = 0.25Subproblem 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 = {0.25, 4}
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