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Simplifying 0 = 140 + 60t + -5t2 Solving 0 = 140 + 60t + -5t2 Solving for variable 't'. Combine like terms: 0 + -140 = -140 -140 + -60t + 5t2 = 140 + 60t + -5t2 + -140 + -60t + 5t2 Reorder the terms: -140 + -60t + 5t2 = 140 + -140 + 60t + -60t + -5t2 + 5t2 Combine like terms: 140 + -140 = 0 -140 + -60t + 5t2 = 0 + 60t + -60t + -5t2 + 5t2 -140 + -60t + 5t2 = 60t + -60t + -5t2 + 5t2 Combine like terms: 60t + -60t = 0 -140 + -60t + 5t2 = 0 + -5t2 + 5t2 -140 + -60t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -140 + -60t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-28 + -12t + t2) = 0 Factor a trinomial. 5((-2 + -1t)(14 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 2
Set the factor '(14 + -1t)' equal to zero and attempt to solve: Simplifying 14 + -1t = 0 Solving 14 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1t = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1t = 0 + -14 -1t = 0 + -14 Combine like terms: 0 + -14 = -14 -1t = -14 Divide each side by '-1'. t = 14 Simplifying t = 14Solution
t = {-2, 14}
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