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Simplifying 1000 = 16t2 + 120t Reorder the terms: 1000 = 120t + 16t2 Solving 1000 = 120t + 16t2 Solving for variable 't'. Reorder the terms: 1000 + -120t + -16t2 = 120t + -120t + 16t2 + -16t2 Combine like terms: 120t + -120t = 0 1000 + -120t + -16t2 = 0 + 16t2 + -16t2 1000 + -120t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 1000 + -120t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(125 + -15t + -2t2) = 0 Factor a trinomial. 8((5 + -1t)(25 + 2t)) = 0 Ignore the factor 8.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 '(25 + 2t)' equal to zero and attempt to solve: Simplifying 25 + 2t = 0 Solving 25 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 2t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 2t = 0 + -25 2t = 0 + -25 Combine like terms: 0 + -25 = -25 2t = -25 Divide each side by '2'. t = -12.5 Simplifying t = -12.5Solution
t = {5, -12.5}
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