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Simplifying 15t2 = -16t2 + 250t Reorder the terms: 15t2 = 250t + -16t2 Solving 15t2 = 250t + -16t2 Solving for variable 't'. Reorder the terms: -250t + 15t2 + 16t2 = 250t + -16t2 + -250t + 16t2 Combine like terms: 15t2 + 16t2 = 31t2 -250t + 31t2 = 250t + -16t2 + -250t + 16t2 Reorder the terms: -250t + 31t2 = 250t + -250t + -16t2 + 16t2 Combine like terms: 250t + -250t = 0 -250t + 31t2 = 0 + -16t2 + 16t2 -250t + 31t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -250t + 31t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-250 + 31t) = 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 '(-250 + 31t)' equal to zero and attempt to solve: Simplifying -250 + 31t = 0 Solving -250 + 31t = 0 Move all terms containing t to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + 31t = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 31t = 0 + 250 31t = 0 + 250 Combine like terms: 0 + 250 = 250 31t = 250 Divide each side by '31'. t = 8.064516129 Simplifying t = 8.064516129Solution
t = {0, 8.064516129}
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