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Simplifying t = -8t2 + 32t Reorder the terms: t = 32t + -8t2 Solving t = 32t + -8t2 Solving for variable 't'. Combine like terms: t + -32t = -31t -31t + 8t2 = 32t + -8t2 + -32t + 8t2 Reorder the terms: -31t + 8t2 = 32t + -32t + -8t2 + 8t2 Combine like terms: 32t + -32t = 0 -31t + 8t2 = 0 + -8t2 + 8t2 -31t + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 -31t + 8t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-31 + 8t) = 0Subproblem 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 '(-31 + 8t)' equal to zero and attempt to solve: Simplifying -31 + 8t = 0 Solving -31 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + 8t = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 8t = 0 + 31 8t = 0 + 31 Combine like terms: 0 + 31 = 31 8t = 31 Divide each side by '8'. t = 3.875 Simplifying t = 3.875Solution
t = {0, 3.875}
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