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Simplifying 96t + -8t2 = 256 Solving 96t + -8t2 = 256 Solving for variable 't'. Reorder the terms: -256 + 96t + -8t2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + 96t + -8t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-32 + 12t + -1t2) = 0 Factor a trinomial. 8((-8 + t)(4 + -1t)) = 0 Ignore the factor 8.Subproblem 1
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 = 8Subproblem 2
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 = 4Solution
t = {8, 4}
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