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Simplifying 45t = -5t2 + 50t Reorder the terms: 45t = 50t + -5t2 Solving 45t = 50t + -5t2 Solving for variable 't'. Combine like terms: 45t + -50t = -5t -5t + 5t2 = 50t + -5t2 + -50t + 5t2 Reorder the terms: -5t + 5t2 = 50t + -50t + -5t2 + 5t2 Combine like terms: 50t + -50t = 0 -5t + 5t2 = 0 + -5t2 + 5t2 -5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -5t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(-1 + 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 '(-1 + t)' equal to zero and attempt to solve: Simplifying -1 + t = 0 Solving -1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + t = 0 + 1 t = 0 + 1 Combine like terms: 0 + 1 = 1 t = 1 Simplifying t = 1Solution
t = {0, 1}
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