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Simplifying 26 = -5t2 + 30t + 1 Reorder the terms: 26 = 1 + 30t + -5t2 Solving 26 = 1 + 30t + -5t2 Solving for variable 't'. Combine like terms: 26 + -1 = 25 25 + -30t + 5t2 = 1 + 30t + -5t2 + -1 + -30t + 5t2 Reorder the terms: 25 + -30t + 5t2 = 1 + -1 + 30t + -30t + -5t2 + 5t2 Combine like terms: 1 + -1 = 0 25 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2 25 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2 Combine like terms: 30t + -30t = 0 25 + -30t + 5t2 = 0 + -5t2 + 5t2 25 + -30t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 25 + -30t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -6t + t2) = 0 Factor a trinomial. 5((1 + -1t)(5 + -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 '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {1, 5}
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