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Simplifying 80 = -5t2 + -5t + 180 Reorder the terms: 80 = 180 + -5t + -5t2 Solving 80 = 180 + -5t + -5t2 Solving for variable 't'. Combine like terms: 80 + -180 = -100 -100 + 5t + 5t2 = 180 + -5t + -5t2 + -180 + 5t + 5t2 Reorder the terms: -100 + 5t + 5t2 = 180 + -180 + -5t + 5t + -5t2 + 5t2 Combine like terms: 180 + -180 = 0 -100 + 5t + 5t2 = 0 + -5t + 5t + -5t2 + 5t2 -100 + 5t + 5t2 = -5t + 5t + -5t2 + 5t2 Combine like terms: -5t + 5t = 0 -100 + 5t + 5t2 = 0 + -5t2 + 5t2 -100 + 5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -100 + 5t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + t + t2) = 0 Factor a trinomial. 5((-5 + -1t)(4 + -1t)) = 0 Ignore the factor 5.Subproblem 1
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 = -5Subproblem 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 = {-5, 4}
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