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