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Simplifying 5 = -16t2 + 128t + 5 Reorder the terms: 5 = 5 + 128t + -16t2 Add '-5' to each side of the equation. 5 + -5 = 5 + 128t + -5 + -16t2 Combine like terms: 5 + -5 = 0 0 = 5 + 128t + -5 + -16t2 Reorder the terms: 0 = 5 + -5 + 128t + -16t2 Combine like terms: 5 + -5 = 0 0 = 0 + 128t + -16t2 0 = 128t + -16t2 Solving 0 = 128t + -16t2 Solving for variable 't'. Remove the zero: -128t + 16t2 = 128t + -16t2 + -128t + 16t2 Reorder the terms: -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 -128t + 16t2 = 0 + -16t2 + 16t2 -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16t'. 16t(-8 + t) = 0 Ignore the factor 16.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 '(-8 + t)' equal to zero and attempt to solve: Simplifying -8 + t = 0 Solving -8 + t = 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 + t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + t = 0 + 8 t = 0 + 8 Combine like terms: 0 + 8 = 8 t = 8 Simplifying t = 8Solution
t = {0, 8}
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