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Simplifying 76 = -16t2 + 160t Reorder the terms: 76 = 160t + -16t2 Solving 76 = 160t + -16t2 Solving for variable 't'. Reorder the terms: 76 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 76 + -160t + 16t2 = 0 + -16t2 + 16t2 76 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 76 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(19 + -40t + 4t2) = 0 Factor a trinomial. 4((1 + -2t)(19 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Subproblem 2
Set the factor '(19 + -2t)' equal to zero and attempt to solve: Simplifying 19 + -2t = 0 Solving 19 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -2t = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -2t = 0 + -19 -2t = 0 + -19 Combine like terms: 0 + -19 = -19 -2t = -19 Divide each side by '-2'. t = 9.5 Simplifying t = 9.5Solution
t = {0.5, 9.5}
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