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Simplifying -16t2 + 104t + 120 = 0 Reorder the terms: 120 + 104t + -16t2 = 0 Solving 120 + 104t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(15 + 13t + -2t2) = 0 Factor a trinomial. 8((15 + -2t)(1 + t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(15 + -2t)' equal to zero and attempt to solve: Simplifying 15 + -2t = 0 Solving 15 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2t = 0 + -15 -2t = 0 + -15 Combine like terms: 0 + -15 = -15 -2t = -15 Divide each side by '-2'. t = 7.5 Simplifying t = 7.5Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {7.5, -1}
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