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Simplifying -16t2 + 2t + 14 = 0 Reorder the terms: 14 + 2t + -16t2 = 0 Solving 14 + 2t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + t + -8t2) = 0 Factor a trinomial. 2((1 + -1t)(7 + 8t)) = 0 Ignore the factor 2.Subproblem 1
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 = 1Subproblem 2
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 = -0.875Solution
t = {1, -0.875}
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