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Simplifying 6t2 = 7 + -19t Solving 6t2 = 7 + -19t Solving for variable 't'. Reorder the terms: -7 + 19t + 6t2 = 7 + -19t + -7 + 19t Reorder the terms: -7 + 19t + 6t2 = 7 + -7 + -19t + 19t Combine like terms: 7 + -7 = 0 -7 + 19t + 6t2 = 0 + -19t + 19t -7 + 19t + 6t2 = -19t + 19t Combine like terms: -19t + 19t = 0 -7 + 19t + 6t2 = 0 Factor a trinomial. (-7 + -2t)(1 + -3t) = 0Subproblem 1
Set the factor '(-7 + -2t)' equal to zero and attempt to solve: Simplifying -7 + -2t = 0 Solving -7 + -2t = 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 + -2t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2t = 0 + 7 -2t = 0 + 7 Combine like terms: 0 + 7 = 7 -2t = 7 Divide each side by '-2'. t = -3.5 Simplifying t = -3.5Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve: Simplifying 1 + -3t = 0 Solving 1 + -3t = 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 + -3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3t = 0 + -1 -3t = 0 + -1 Combine like terms: 0 + -1 = -1 -3t = -1 Divide each side by '-3'. t = 0.3333333333 Simplifying t = 0.3333333333Solution
t = {-3.5, 0.3333333333}
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