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Simplifying 0 = -16t2 + 96t + 256 Reorder the terms: 0 = 256 + 96t + -16t2 Solving 0 = 256 + 96t + -16t2 Solving for variable 't'. Combine like terms: 0 + -256 = -256 -256 + -96t + 16t2 = 256 + 96t + -16t2 + -256 + -96t + 16t2 Reorder the terms: -256 + -96t + 16t2 = 256 + -256 + 96t + -96t + -16t2 + 16t2 Combine like terms: 256 + -256 = 0 -256 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -256 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -256 + -96t + 16t2 = 0 + -16t2 + 16t2 -256 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -256 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-16 + -6t + t2) = 0 Factor a trinomial. 16((-2 + -1t)(8 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 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 = {-2, 8}
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