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Simplifying 16t2 + 10t = 174 Reorder the terms: 10t + 16t2 = 174 Solving 10t + 16t2 = 174 Solving for variable 't'. Reorder the terms: -174 + 10t + 16t2 = 174 + -174 Combine like terms: 174 + -174 = 0 -174 + 10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-87 + 5t + 8t2) = 0 Factor a trinomial. 2((-29 + -8t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -8t)' equal to zero and attempt to solve: Simplifying -29 + -8t = 0 Solving -29 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + -8t = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -8t = 0 + 29 -8t = 0 + 29 Combine like terms: 0 + 29 = 29 -8t = 29 Divide each side by '-8'. t = -3.625 Simplifying t = -3.625Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-3.625, 3}
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