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Simplifying 100 = -5t2 + 40t + 100 Reorder the terms: 100 = 100 + 40t + -5t2 Add '-100' to each side of the equation. 100 + -100 = 100 + 40t + -100 + -5t2 Combine like terms: 100 + -100 = 0 0 = 100 + 40t + -100 + -5t2 Reorder the terms: 0 = 100 + -100 + 40t + -5t2 Combine like terms: 100 + -100 = 0 0 = 0 + 40t + -5t2 0 = 40t + -5t2 Solving 0 = 40t + -5t2 Solving for variable 't'. Remove the zero: -40t + 5t2 = 40t + -5t2 + -40t + 5t2 Reorder the terms: -40t + 5t2 = 40t + -40t + -5t2 + 5t2 Combine like terms: 40t + -40t = 0 -40t + 5t2 = 0 + -5t2 + 5t2 -40t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -40t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(-8 + t) = 0 Ignore the factor 5.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 '(-8 + t)' equal to zero and attempt to solve: Simplifying -8 + t = 0 Solving -8 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + t = 0 + 8 t = 0 + 8 Combine like terms: 0 + 8 = 8 t = 8 Simplifying t = 8Solution
t = {0, 8}
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