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Simplifying 1024 = 256t + -16t2 Solving 1024 = 256t + -16t2 Solving for variable 't'. Reorder the terms: 1024 + -256t + 16t2 = 256t + -256t + -16t2 + 16t2 Combine like terms: 256t + -256t = 0 1024 + -256t + 16t2 = 0 + -16t2 + 16t2 1024 + -256t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1024 + -256t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(64 + -16t + t2) = 0 Factor a trinomial. 16((8 + -1t)(8 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {8, 8}
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