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Simplifying 560 = -16t2 + 104t + 560 Reorder the terms: 560 = 560 + 104t + -16t2 Add '-560' to each side of the equation. 560 + -560 = 560 + 104t + -560 + -16t2 Combine like terms: 560 + -560 = 0 0 = 560 + 104t + -560 + -16t2 Reorder the terms: 0 = 560 + -560 + 104t + -16t2 Combine like terms: 560 + -560 = 0 0 = 0 + 104t + -16t2 0 = 104t + -16t2 Solving 0 = 104t + -16t2 Solving for variable 't'. Remove the zero: -104t + 16t2 = 104t + -16t2 + -104t + 16t2 Reorder the terms: -104t + 16t2 = 104t + -104t + -16t2 + 16t2 Combine like terms: 104t + -104t = 0 -104t + 16t2 = 0 + -16t2 + 16t2 -104t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -104t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8t'. 8t(-13 + 2t) = 0 Ignore the factor 8.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-13 + 2t)' equal to zero and attempt to solve: Simplifying -13 + 2t = 0 Solving -13 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 2t = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2t = 0 + 13 2t = 0 + 13 Combine like terms: 0 + 13 = 13 2t = 13 Divide each side by '2'. t = 6.5 Simplifying t = 6.5Solution
t = {0, 6.5}
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