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Simplifying 8t2 = -16t + 504 Reorder the terms: 8t2 = 504 + -16t Solving 8t2 = 504 + -16t Solving for variable 't'. Reorder the terms: -504 + 16t + 8t2 = 504 + -16t + -504 + 16t Reorder the terms: -504 + 16t + 8t2 = 504 + -504 + -16t + 16t Combine like terms: 504 + -504 = 0 -504 + 16t + 8t2 = 0 + -16t + 16t -504 + 16t + 8t2 = -16t + 16t Combine like terms: -16t + 16t = 0 -504 + 16t + 8t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-63 + 2t + t2) = 0 Factor a trinomial. 8((-9 + -1t)(7 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve: Simplifying -9 + -1t = 0 Solving -9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1t = 0 + 9 -1t = 0 + 9 Combine like terms: 0 + 9 = 9 -1t = 9 Divide each side by '-1'. t = -9 Simplifying t = -9Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-9, 7}
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