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Simplifying t(6t + 25) = -25 Reorder the terms: t(25 + 6t) = -25 (25 * t + 6t * t) = -25 (25t + 6t2) = -25 Solving 25t + 6t2 = -25 Solving for variable 't'. Reorder the terms: 25 + 25t + 6t2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 25t + 6t2 = 0 Factor a trinomial. (5 + 2t)(5 + 3t) = 0Subproblem 1
Set the factor '(5 + 2t)' equal to zero and attempt to solve: Simplifying 5 + 2t = 0 Solving 5 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2t = 0 + -5 2t = 0 + -5 Combine like terms: 0 + -5 = -5 2t = -5 Divide each side by '2'. t = -2.5 Simplifying t = -2.5Subproblem 2
Set the factor '(5 + 3t)' equal to zero and attempt to solve: Simplifying 5 + 3t = 0 Solving 5 + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3t = 0 + -5 3t = 0 + -5 Combine like terms: 0 + -5 = -5 3t = -5 Divide each side by '3'. t = -1.666666667 Simplifying t = -1.666666667Solution
t = {-2.5, -1.666666667}
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