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Simplifying -16t2 + 2000t + -40000 = 0 Reorder the terms: -40000 + 2000t + -16t2 = 0 Solving -40000 + 2000t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-2500 + 125t + -1t2) = 0 Factor a trinomial. 16((-100 + t)(25 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-100 + t)' equal to zero and attempt to solve: Simplifying -100 + t = 0 Solving -100 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + t = 0 + 100 Combine like terms: -100 + 100 = 0 0 + t = 0 + 100 t = 0 + 100 Combine like terms: 0 + 100 = 100 t = 100 Simplifying t = 100Subproblem 2
Set the factor '(25 + -1t)' equal to zero and attempt to solve: Simplifying 25 + -1t = 0 Solving 25 + -1t = 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 + -1t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1t = 0 + -25 -1t = 0 + -25 Combine like terms: 0 + -25 = -25 -1t = -25 Divide each side by '-1'. t = 25 Simplifying t = 25Solution
t = {100, 25}
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