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Simplifying 85 = 90t + -5t2 Solving 85 = 90t + -5t2 Solving for variable 't'. Reorder the terms: 85 + -90t + 5t2 = 90t + -90t + -5t2 + 5t2 Combine like terms: 90t + -90t = 0 85 + -90t + 5t2 = 0 + -5t2 + 5t2 85 + -90t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 85 + -90t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(17 + -18t + t2) = 0 Factor a trinomial. 5((1 + -1t)(17 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(17 + -1t)' equal to zero and attempt to solve: Simplifying 17 + -1t = 0 Solving 17 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1t = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1t = 0 + -17 -1t = 0 + -17 Combine like terms: 0 + -17 = -17 -1t = -17 Divide each side by '-1'. t = 17 Simplifying t = 17Solution
t = {1, 17}
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