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Simplifying 176 = -16t2 + 114t + 6 Reorder the terms: 176 = 6 + 114t + -16t2 Solving 176 = 6 + 114t + -16t2 Solving for variable 't'. Combine like terms: 176 + -6 = 170 170 + -114t + 16t2 = 6 + 114t + -16t2 + -6 + -114t + 16t2 Reorder the terms: 170 + -114t + 16t2 = 6 + -6 + 114t + -114t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 170 + -114t + 16t2 = 0 + 114t + -114t + -16t2 + 16t2 170 + -114t + 16t2 = 114t + -114t + -16t2 + 16t2 Combine like terms: 114t + -114t = 0 170 + -114t + 16t2 = 0 + -16t2 + 16t2 170 + -114t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 170 + -114t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(85 + -57t + 8t2) = 0 Factor a trinomial. 2((17 + -8t)(5 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -8t)' equal to zero and attempt to solve: Simplifying 17 + -8t = 0 Solving 17 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -8t = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -8t = 0 + -17 -8t = 0 + -17 Combine like terms: 0 + -17 = -17 -8t = -17 Divide each side by '-8'. t = 2.125 Simplifying t = 2.125Subproblem 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 = {2.125, 5}
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