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Simplifying Sn = -2n2 + not Reorder the terms: nS = not + -2n2 Solving nS = not + -2n2 Solving for variable 'n'. Reorder the terms: nS + -1not + 2n2 = not + -1not + -2n2 + 2n2 Combine like terms: not + -1not = 0 nS + -1not + 2n2 = 0 + -2n2 + 2n2 nS + -1not + 2n2 = -2n2 + 2n2 Combine like terms: -2n2 + 2n2 = 0 nS + -1not + 2n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(S + -1ot + 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 '(S + -1ot + 2n)' equal to zero and attempt to solve: Simplifying S + -1ot + 2n = 0 Reorder the terms: S + 2n + -1ot = 0 Solving S + 2n + -1ot = 0 Move all terms containing n to the left, all other terms to the right. Add '-1S' to each side of the equation. S + 2n + -1S + -1ot = 0 + -1S Reorder the terms: S + -1S + 2n + -1ot = 0 + -1S Combine like terms: S + -1S = 0 0 + 2n + -1ot = 0 + -1S 2n + -1ot = 0 + -1S Remove the zero: 2n + -1ot = -1S Add 'ot' to each side of the equation. 2n + -1ot + ot = -1S + ot Combine like terms: -1ot + ot = 0 2n + 0 = -1S + ot 2n = -1S + ot Divide each side by '2'. n = -0.5S + 0.5ot Simplifying n = -0.5S + 0.5otSolution
n = {0, -0.5S + 0.5ot}
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