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Simplifying 0 = 16t2 + -104t + -56 Reorder the terms: 0 = -56 + -104t + 16t2 Solving 0 = -56 + -104t + 16t2 Solving for variable 't'. Combine like terms: 0 + 56 = 56 56 + 104t + -16t2 = -56 + -104t + 16t2 + 56 + 104t + -16t2 Reorder the terms: 56 + 104t + -16t2 = -56 + 56 + -104t + 104t + 16t2 + -16t2 Combine like terms: -56 + 56 = 0 56 + 104t + -16t2 = 0 + -104t + 104t + 16t2 + -16t2 56 + 104t + -16t2 = -104t + 104t + 16t2 + -16t2 Combine like terms: -104t + 104t = 0 56 + 104t + -16t2 = 0 + 16t2 + -16t2 56 + 104t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 56 + 104t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(7 + 13t + -2t2) = 0 Factor a trinomial. 8((7 + -1t)(1 + 2t)) = 0 Ignore the factor 8.Subproblem 1
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 = 7Subproblem 2
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 = -0.5Solution
t = {7, -0.5}
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