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Simplifying 126 = -16t2 + 90t Reorder the terms: 126 = 90t + -16t2 Solving 126 = 90t + -16t2 Solving for variable 't'. Reorder the terms: 126 + -90t + 16t2 = 90t + -90t + -16t2 + 16t2 Combine like terms: 90t + -90t = 0 126 + -90t + 16t2 = 0 + -16t2 + 16t2 126 + -90t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 126 + -90t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(63 + -45t + 8t2) = 0 Factor a trinomial. 2((21 + -8t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + -8t)' equal to zero and attempt to solve: Simplifying 21 + -8t = 0 Solving 21 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -8t = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -8t = 0 + -21 -8t = 0 + -21 Combine like terms: 0 + -21 = -21 -8t = -21 Divide each side by '-8'. t = 2.625 Simplifying t = 2.625Subproblem 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 = {2.625, 3}
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