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Simplifying 120 = -16t2 + 56t + 240 Reorder the terms: 120 = 240 + 56t + -16t2 Solving 120 = 240 + 56t + -16t2 Solving for variable 't'. Combine like terms: 120 + -240 = -120 -120 + -56t + 16t2 = 240 + 56t + -16t2 + -240 + -56t + 16t2 Reorder the terms: -120 + -56t + 16t2 = 240 + -240 + 56t + -56t + -16t2 + 16t2 Combine like terms: 240 + -240 = 0 -120 + -56t + 16t2 = 0 + 56t + -56t + -16t2 + 16t2 -120 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2 Combine like terms: 56t + -56t = 0 -120 + -56t + 16t2 = 0 + -16t2 + 16t2 -120 + -56t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -120 + -56t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-15 + -7t + 2t2) = 0 Factor a trinomial. 8((-3 + -2t)(5 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -2t)' equal to zero and attempt to solve: Simplifying -3 + -2t = 0 Solving -3 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2t = 0 + 3 -2t = 0 + 3 Combine like terms: 0 + 3 = 3 -2t = 3 Divide each side by '-2'. t = -1.5 Simplifying t = -1.5Subproblem 2
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 = 5Solution
t = {-1.5, 5}
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