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Simplifying 45 = -5t2 + 30t + 80 Reorder the terms: 45 = 80 + 30t + -5t2 Solving 45 = 80 + 30t + -5t2 Solving for variable 't'. Combine like terms: 45 + -80 = -35 -35 + -30t + 5t2 = 80 + 30t + -5t2 + -80 + -30t + 5t2 Reorder the terms: -35 + -30t + 5t2 = 80 + -80 + 30t + -30t + -5t2 + 5t2 Combine like terms: 80 + -80 = 0 -35 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2 -35 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2 Combine like terms: 30t + -30t = 0 -35 + -30t + 5t2 = 0 + -5t2 + 5t2 -35 + -30t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -35 + -30t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-7 + -6t + t2) = 0 Factor a trinomial. 5((-1 + -1t)(7 + -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 '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-1, 7}
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