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Simplifying 20 = -16t2 + 84t Reorder the terms: 20 = 84t + -16t2 Solving 20 = 84t + -16t2 Solving for variable 't'. Reorder the terms: 20 + -84t + 16t2 = 84t + -84t + -16t2 + 16t2 Combine like terms: 84t + -84t = 0 20 + -84t + 16t2 = 0 + -16t2 + 16t2 20 + -84t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -84t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -21t + 4t2) = 0 Factor a trinomial. 4((1 + -4t)(5 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {0.25, 5}
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