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Simplifying -16t2 + 250t = 900 Reorder the terms: 250t + -16t2 = 900 Solving 250t + -16t2 = 900 Solving for variable 't'. Reorder the terms: -900 + 250t + -16t2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 250t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-450 + 125t + -8t2) = 0 Factor a trinomial. 2((-10 + t)(45 + -8t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + t)' equal to zero and attempt to solve: Simplifying -10 + t = 0 Solving -10 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + t = 0 + 10 t = 0 + 10 Combine like terms: 0 + 10 = 10 t = 10 Simplifying t = 10Subproblem 2
Set the factor '(45 + -8t)' equal to zero and attempt to solve: Simplifying 45 + -8t = 0 Solving 45 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + -8t = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -8t = 0 + -45 -8t = 0 + -45 Combine like terms: 0 + -45 = -45 -8t = -45 Divide each side by '-8'. t = 5.625 Simplifying t = 5.625Solution
t = {10, 5.625}
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