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