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Simplifying 6t2 + 17t + 7 = 0 Reorder the terms: 7 + 17t + 6t2 = 0 Solving 7 + 17t + 6t2 = 0 Solving for variable 't'. Factor a trinomial. (7 + 3t)(1 + 2t) = 0Subproblem 1
Set the factor '(7 + 3t)' equal to zero and attempt to solve: Simplifying 7 + 3t = 0 Solving 7 + 3t = 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 + 3t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3t = 0 + -7 3t = 0 + -7 Combine like terms: 0 + -7 = -7 3t = -7 Divide each side by '3'. t = -2.333333333 Simplifying t = -2.333333333Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve: Simplifying 1 + 2t = 0 Solving 1 + 2t = 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 + 2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2t = 0 + -1 2t = 0 + -1 Combine like terms: 0 + -1 = -1 2t = -1 Divide each side by '2'. t = -0.5 Simplifying t = -0.5Solution
t = {-2.333333333, -0.5}
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