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Simplifying 1024 = -16t2 + 320t + 0 Reorder the terms: 1024 = 0 + 320t + -16t2 Remove the zero: 1024 = 320t + -16t2 Solving 1024 = 320t + -16t2 Solving for variable 't'. Reorder the terms: 1024 + -320t + 16t2 = 320t + -320t + -16t2 + 16t2 Combine like terms: 320t + -320t = 0 1024 + -320t + 16t2 = 0 + -16t2 + 16t2 1024 + -320t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1024 + -320t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(64 + -20t + t2) = 0 Factor a trinomial. 16((4 + -1t)(16 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Subproblem 2
Set the factor '(16 + -1t)' equal to zero and attempt to solve: Simplifying 16 + -1t = 0 Solving 16 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1t = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1t = 0 + -16 -1t = 0 + -16 Combine like terms: 0 + -16 = -16 -1t = -16 Divide each side by '-1'. t = 16 Simplifying t = 16Solution
t = {4, 16}
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