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Simplifying 0 = -16t2 + -8t + 120 Reorder the terms: 0 = 120 + -8t + -16t2 Solving 0 = 120 + -8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -120 = -120 -120 + 8t + 16t2 = 120 + -8t + -16t2 + -120 + 8t + 16t2 Reorder the terms: -120 + 8t + 16t2 = 120 + -120 + -8t + 8t + -16t2 + 16t2 Combine like terms: 120 + -120 = 0 -120 + 8t + 16t2 = 0 + -8t + 8t + -16t2 + 16t2 -120 + 8t + 16t2 = -8t + 8t + -16t2 + 16t2 Combine like terms: -8t + 8t = 0 -120 + 8t + 16t2 = 0 + -16t2 + 16t2 -120 + 8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -120 + 8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-15 + t + 2t2) = 0 Factor a trinomial. 8((-3 + -1t)(5 + -2t)) = 0 Ignore the factor 8.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 '(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 = {-3, 2.5}
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