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Simplifying 25 = -6t2 + 30t + 1 Reorder the terms: 25 = 1 + 30t + -6t2 Solving 25 = 1 + 30t + -6t2 Solving for variable 't'. Combine like terms: 25 + -1 = 24 24 + -30t + 6t2 = 1 + 30t + -6t2 + -1 + -30t + 6t2 Reorder the terms: 24 + -30t + 6t2 = 1 + -1 + 30t + -30t + -6t2 + 6t2 Combine like terms: 1 + -1 = 0 24 + -30t + 6t2 = 0 + 30t + -30t + -6t2 + 6t2 24 + -30t + 6t2 = 30t + -30t + -6t2 + 6t2 Combine like terms: 30t + -30t = 0 24 + -30t + 6t2 = 0 + -6t2 + 6t2 24 + -30t + 6t2 = -6t2 + 6t2 Combine like terms: -6t2 + 6t2 = 0 24 + -30t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -5t + t2) = 0 Factor a trinomial. 6((1 + -1t)(4 + -1t)) = 0 Ignore the factor 6.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 '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {1, 4}
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