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Simplifying 14 = -16t2 + 30t Reorder the terms: 14 = 30t + -16t2 Solving 14 = 30t + -16t2 Solving for variable 't'. Reorder the terms: 14 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 14 + -30t + 16t2 = 0 + -16t2 + 16t2 14 + -30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 14 + -30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -15t + 8t2) = 0 Factor a trinomial. 2((7 + -8t)(1 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -8t)' equal to zero and attempt to solve: Simplifying 7 + -8t = 0 Solving 7 + -8t = 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 + -8t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8t = 0 + -7 -8t = 0 + -7 Combine like terms: 0 + -7 = -7 -8t = -7 Divide each side by '-8'. t = 0.875 Simplifying t = 0.875Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0.875, 1}
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