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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((-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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