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Simplifying 8000 = -16t2 + 500t + 8000 Reorder the terms: 8000 = 8000 + 500t + -16t2 Add '-8000' to each side of the equation. 8000 + -8000 = 8000 + 500t + -8000 + -16t2 Combine like terms: 8000 + -8000 = 0 0 = 8000 + 500t + -8000 + -16t2 Reorder the terms: 0 = 8000 + -8000 + 500t + -16t2 Combine like terms: 8000 + -8000 = 0 0 = 0 + 500t + -16t2 0 = 500t + -16t2 Solving 0 = 500t + -16t2 Solving for variable 't'. Remove the zero: -500t + 16t2 = 500t + -16t2 + -500t + 16t2 Reorder the terms: -500t + 16t2 = 500t + -500t + -16t2 + 16t2 Combine like terms: 500t + -500t = 0 -500t + 16t2 = 0 + -16t2 + 16t2 -500t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -500t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-125 + 4t) = 0 Ignore the factor 4.Subproblem 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 '(-125 + 4t)' equal to zero and attempt to solve: Simplifying -125 + 4t = 0 Solving -125 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + 4t = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 4t = 0 + 125 4t = 0 + 125 Combine like terms: 0 + 125 = 125 4t = 125 Divide each side by '4'. t = 31.25 Simplifying t = 31.25Solution
t = {0, 31.25}
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