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Simplifying P(t) = 5t2 + -20t Multiply P * t tP = 5t2 + -20t Reorder the terms: tP = -20t + 5t2 Solving tP = -20t + 5t2 Solving for variable 't'. Reorder the terms: 20t + tP + -5t2 = -20t + 5t2 + 20t + -5t2 Reorder the terms: 20t + tP + -5t2 = -20t + 20t + 5t2 + -5t2 Combine like terms: -20t + 20t = 0 20t + tP + -5t2 = 0 + 5t2 + -5t2 20t + tP + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 20t + tP + -5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(20 + P + -5t) = 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 + P + -5t)' equal to zero and attempt to solve: Simplifying 20 + P + -5t = 0 Solving 20 + P + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + P + -20 + -5t = 0 + -20 Reorder the terms: 20 + -20 + P + -5t = 0 + -20 Combine like terms: 20 + -20 = 0 0 + P + -5t = 0 + -20 P + -5t = 0 + -20 Combine like terms: 0 + -20 = -20 P + -5t = -20 Add '-1P' to each side of the equation. P + -1P + -5t = -20 + -1P Combine like terms: P + -1P = 0 0 + -5t = -20 + -1P -5t = -20 + -1P Divide each side by '-5'. t = 4 + 0.2P Simplifying t = 4 + 0.2PSolution
t = {0, 4 + 0.2P}
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