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Simplifying 0 = -16t2 + 16t + 60 Reorder the terms: 0 = 60 + 16t + -16t2 Solving 0 = 60 + 16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -60 = -60 -60 + -16t + 16t2 = 60 + 16t + -16t2 + -60 + -16t + 16t2 Reorder the terms: -60 + -16t + 16t2 = 60 + -60 + 16t + -16t + -16t2 + 16t2 Combine like terms: 60 + -60 = 0 -60 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -60 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -60 + -16t + 16t2 = 0 + -16t2 + 16t2 -60 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -60 + -16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -4t + 4t2) = 0 Factor a trinomial. 4((-3 + -2t)(5 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -2t)' equal to zero and attempt to solve: Simplifying -3 + -2t = 0 Solving -3 + -2t = 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 + -2t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2t = 0 + 3 -2t = 0 + 3 Combine like terms: 0 + 3 = 3 -2t = 3 Divide each side by '-2'. t = -1.5 Simplifying t = -1.5Subproblem 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 = {-1.5, 2.5}
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