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Simplifying N(t) = 20t + -1t2 Multiply N * t tN = 20t + -1t2 Solving tN = 20t + -1t2 Solving for variable 't'. Reorder the terms: -20t + tN + t2 = 20t + -1t2 + -20t + t2 Reorder the terms: -20t + tN + t2 = 20t + -20t + -1t2 + t2 Combine like terms: 20t + -20t = 0 -20t + tN + t2 = 0 + -1t2 + t2 -20t + tN + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -20t + tN + t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-20 + N + t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-20 + N + t)' equal to zero and attempt to solve: Simplifying -20 + N + t = 0 Solving -20 + N + t = 0 Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + N + 20 + t = 0 + 20 Reorder the terms: -20 + 20 + N + t = 0 + 20 Combine like terms: -20 + 20 = 0 0 + N + t = 0 + 20 N + t = 0 + 20 Combine like terms: 0 + 20 = 20 N + t = 20 Add '-1N' to each side of the equation. N + -1N + t = 20 + -1N Combine like terms: N + -1N = 0 0 + t = 20 + -1N t = 20 + -1N Simplifying t = 20 + -1NSolution
t = {0, 20 + -1N}
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