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Simplifying 204 = 20t + 16t2 Solving 204 = 20t + 16t2 Solving for variable 't'. Reorder the terms: 204 + -20t + -16t2 = 20t + -20t + 16t2 + -16t2 Combine like terms: 20t + -20t = 0 204 + -20t + -16t2 = 0 + 16t2 + -16t2 204 + -20t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 204 + -20t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(51 + -5t + -4t2) = 0 Factor a trinomial. 4((3 + -1t)(17 + 4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Subproblem 2
Set the factor '(17 + 4t)' equal to zero and attempt to solve: Simplifying 17 + 4t = 0 Solving 17 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 4t = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 4t = 0 + -17 4t = 0 + -17 Combine like terms: 0 + -17 = -17 4t = -17 Divide each side by '4'. t = -4.25 Simplifying t = -4.25Solution
t = {3, -4.25}
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