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Simplifying 8n2 + 16n + -2 = 8 Reorder the terms: -2 + 16n + 8n2 = 8 Solving -2 + 16n + 8n2 = 8 Solving for variable 'n'. Reorder the terms: -2 + -8 + 16n + 8n2 = 8 + -8 Combine like terms: -2 + -8 = -10 -10 + 16n + 8n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -10 + 16n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 8n + 4n2) = 0 Factor a trinomial. 2((-5 + -2n)(1 + -2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve: Simplifying -5 + -2n = 0 Solving -5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2n = 0 + 5 -2n = 0 + 5 Combine like terms: 0 + 5 = 5 -2n = 5 Divide each side by '-2'. n = -2.5 Simplifying n = -2.5Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-2.5, 0.5}
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