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Simplifying T(n) = 2n(n + 5) Multiply T * n nT = 2n(n + 5) Reorder the terms: nT = 2n(5 + n) nT = (5 * 2n + n * 2n) nT = (10n + 2n2) Solving nT = 10n + 2n2 Solving for variable 'n'. Reorder the terms: -10n + nT + -2n2 = 10n + 2n2 + -10n + -2n2 Reorder the terms: -10n + nT + -2n2 = 10n + -10n + 2n2 + -2n2 Combine like terms: 10n + -10n = 0 -10n + nT + -2n2 = 0 + 2n2 + -2n2 -10n + nT + -2n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 -10n + nT + -2n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-10 + T + -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 '(-10 + T + -2n)' equal to zero and attempt to solve: Simplifying -10 + T + -2n = 0 Solving -10 + T + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + T + 10 + -2n = 0 + 10 Reorder the terms: -10 + 10 + T + -2n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + T + -2n = 0 + 10 T + -2n = 0 + 10 Combine like terms: 0 + 10 = 10 T + -2n = 10 Add '-1T' to each side of the equation. T + -1T + -2n = 10 + -1T Combine like terms: T + -1T = 0 0 + -2n = 10 + -1T -2n = 10 + -1T Divide each side by '-2'. n = -5 + 0.5T Simplifying n = -5 + 0.5TSolution
n = {0, -5 + 0.5T}
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