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Simplifying 162 = -16t2 + 162t Reorder the terms: 162 = 162t + -16t2 Solving 162 = 162t + -16t2 Solving for variable 't'. Reorder the terms: 162 + -162t + 16t2 = 162t + -162t + -16t2 + 16t2 Combine like terms: 162t + -162t = 0 162 + -162t + 16t2 = 0 + -16t2 + 16t2 162 + -162t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 162 + -162t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -81t + 8t2) = 0 Factor a trinomial. 2((9 + -8t)(9 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -8t)' equal to zero and attempt to solve: Simplifying 9 + -8t = 0 Solving 9 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -8t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8t = 0 + -9 -8t = 0 + -9 Combine like terms: 0 + -9 = -9 -8t = -9 Divide each side by '-8'. t = 1.125 Simplifying t = 1.125Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {1.125, 9}
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