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Simplifying 504 = -16t2 + 46t + 576 Reorder the terms: 504 = 576 + 46t + -16t2 Solving 504 = 576 + 46t + -16t2 Solving for variable 't'. Combine like terms: 504 + -576 = -72 -72 + -46t + 16t2 = 576 + 46t + -16t2 + -576 + -46t + 16t2 Reorder the terms: -72 + -46t + 16t2 = 576 + -576 + 46t + -46t + -16t2 + 16t2 Combine like terms: 576 + -576 = 0 -72 + -46t + 16t2 = 0 + 46t + -46t + -16t2 + 16t2 -72 + -46t + 16t2 = 46t + -46t + -16t2 + 16t2 Combine like terms: 46t + -46t = 0 -72 + -46t + 16t2 = 0 + -16t2 + 16t2 -72 + -46t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -72 + -46t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + -23t + 8t2) = 0 Factor a trinomial. 2((-9 + -8t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -8t)' equal to zero and attempt to solve: Simplifying -9 + -8t = 0 Solving -9 + -8t = 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 + -8t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -8t = 0 + 9 -8t = 0 + 9 Combine like terms: 0 + 9 = 9 -8t = 9 Divide each side by '-8'. t = -1.125 Simplifying t = -1.125Subproblem 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 = {-1.125, 4}
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