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Simplifying 500t = -16t2 + 200t + 0 Reorder the terms: 500t = 0 + 200t + -16t2 Remove the zero: 500t = 200t + -16t2 Solving 500t = 200t + -16t2 Solving for variable 't'. Combine like terms: 500t + -200t = 300t 300t + 16t2 = 200t + -16t2 + -200t + 16t2 Reorder the terms: 300t + 16t2 = 200t + -200t + -16t2 + 16t2 Combine like terms: 200t + -200t = 0 300t + 16t2 = 0 + -16t2 + 16t2 300t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 300t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(75 + 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 '(75 + 4t)' equal to zero and attempt to solve: Simplifying 75 + 4t = 0 Solving 75 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + 4t = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 4t = 0 + -75 4t = 0 + -75 Combine like terms: 0 + -75 = -75 4t = -75 Divide each side by '4'. t = -18.75 Simplifying t = -18.75Solution
t = {0, -18.75}
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