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Simplifying 84 = 80t + -16t2 Solving 84 = 80t + -16t2 Solving for variable 't'. Reorder the terms: 84 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 84 + -80t + 16t2 = 0 + -16t2 + 16t2 84 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 84 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(21 + -20t + 4t2) = 0 Factor a trinomial. 4((3 + -2t)(7 + -2t)) = 0 Ignore the factor 4.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 '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Solution
t = {1.5, 3.5}
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