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Simplifying -16t2 + 240t = 500 Reorder the terms: 240t + -16t2 = 500 Solving 240t + -16t2 = 500 Solving for variable 't'. Reorder the terms: -500 + 240t + -16t2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 240t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-125 + 60t + -4t2) = 0 Factor a trinomial. 4((-25 + 2t)(5 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + 2t)' equal to zero and attempt to solve: Simplifying -25 + 2t = 0 Solving -25 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 2t = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2t = 0 + 25 2t = 0 + 25 Combine like terms: 0 + 25 = 25 2t = 25 Divide each side by '2'. t = 12.5 Simplifying t = 12.5Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {12.5, 2.5}
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