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Simplifying 500t = -16t2 + 25t + 0 Reorder the terms: 500t = 0 + 25t + -16t2 Remove the zero: 500t = 25t + -16t2 Solving 500t = 25t + -16t2 Solving for variable 't'. Combine like terms: 500t + -25t = 475t 475t + 16t2 = 25t + -16t2 + -25t + 16t2 Reorder the terms: 475t + 16t2 = 25t + -25t + -16t2 + 16t2 Combine like terms: 25t + -25t = 0 475t + 16t2 = 0 + -16t2 + 16t2 475t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 475t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(475 + 16t) = 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 '(475 + 16t)' equal to zero and attempt to solve: Simplifying 475 + 16t = 0 Solving 475 + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '-475' to each side of the equation. 475 + -475 + 16t = 0 + -475 Combine like terms: 475 + -475 = 0 0 + 16t = 0 + -475 16t = 0 + -475 Combine like terms: 0 + -475 = -475 16t = -475 Divide each side by '16'. t = -29.6875 Simplifying t = -29.6875Solution
t = {0, -29.6875}
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