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Simplifying 56 = -16t2 + 120t Reorder the terms: 56 = 120t + -16t2 Solving 56 = 120t + -16t2 Solving for variable 't'. Reorder the terms: 56 + -120t + 16t2 = 120t + -120t + -16t2 + 16t2 Combine like terms: 120t + -120t = 0 56 + -120t + 16t2 = 0 + -16t2 + 16t2 56 + -120t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 56 + -120t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(7 + -15t + 2t2) = 0 Factor a trinomial. 8((1 + -2t)(7 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 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 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {0.5, 7}
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