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Simplifying 20t + -4t3 = 4t3 + -20t Reorder the terms: 20t + -4t3 = -20t + 4t3 Solving 20t + -4t3 = -20t + 4t3 Solving for variable 't'. Reorder the terms: 20t + 20t + -4t3 + -4t3 = -20t + 4t3 + 20t + -4t3 Combine like terms: 20t + 20t = 40t 40t + -4t3 + -4t3 = -20t + 4t3 + 20t + -4t3 Combine like terms: -4t3 + -4t3 = -8t3 40t + -8t3 = -20t + 4t3 + 20t + -4t3 Reorder the terms: 40t + -8t3 = -20t + 20t + 4t3 + -4t3 Combine like terms: -20t + 20t = 0 40t + -8t3 = 0 + 4t3 + -4t3 40t + -8t3 = 4t3 + -4t3 Combine like terms: 4t3 + -4t3 = 0 40t + -8t3 = 0 Factor out the Greatest Common Factor (GCF), '8t'. 8t(5 + -1t2) = 0 Ignore the factor 8.Subproblem 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 '(5 + -1t2)' equal to zero and attempt to solve: Simplifying 5 + -1t2 = 0 Solving 5 + -1t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t2 = 0 + -5 -1t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1t2 = -5 Divide each side by '-1'. t2 = 5 Simplifying t2 = 5 Take the square root of each side: t = {-2.236067978, 2.236067978}Solution
t = {0, -2.236067978, 2.236067978}
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