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Simplifying 140 = 80t + -5t2 Solving 140 = 80t + -5t2 Solving for variable 't'. Reorder the terms: 140 + -80t + 5t2 = 80t + -80t + -5t2 + 5t2 Combine like terms: 80t + -80t = 0 140 + -80t + 5t2 = 0 + -5t2 + 5t2 140 + -80t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 140 + -80t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(28 + -16t + 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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