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Simplifying 54 = -16t2 + 60t + 4 Reorder the terms: 54 = 4 + 60t + -16t2 Solving 54 = 4 + 60t + -16t2 Solving for variable 't'. Combine like terms: 54 + -4 = 50 50 + -60t + 16t2 = 4 + 60t + -16t2 + -4 + -60t + 16t2 Reorder the terms: 50 + -60t + 16t2 = 4 + -4 + 60t + -60t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 50 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2 50 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 50 + -60t + 16t2 = 0 + -16t2 + 16t2 50 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 50 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -30t + 8t2) = 0 Factor a trinomial. 2((5 + -4t)(5 + -2t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -4t)' equal to zero and attempt to solve: Simplifying 5 + -4t = 0 Solving 5 + -4t = 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 + -4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t = 0 + -5 -4t = 0 + -5 Combine like terms: 0 + -5 = -5 -4t = -5 Divide each side by '-4'. t = 1.25 Simplifying t = 1.25Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {1.25, 2.5}
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