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Simplifying 400 = 120t + -5t2 Solving 400 = 120t + -5t2 Solving for variable 't'. Reorder the terms: 400 + -120t + 5t2 = 120t + -120t + -5t2 + 5t2 Combine like terms: 120t + -120t = 0 400 + -120t + 5t2 = 0 + -5t2 + 5t2 400 + -120t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 400 + -120t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(80 + -24t + t2) = 0 Factor a trinomial. 5((4 + -1t)(20 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Subproblem 2
Set the factor '(20 + -1t)' equal to zero and attempt to solve: Simplifying 20 + -1t = 0 Solving 20 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1t = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1t = 0 + -20 -1t = 0 + -20 Combine like terms: 0 + -20 = -20 -1t = -20 Divide each side by '-1'. t = 20 Simplifying t = 20Solution
t = {4, 20}
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