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Simplifying 0 = 6t2 + -13tv + -5v2 Reorder the terms: 0 = -13tv + 6t2 + -5v2 Solving 0 = -13tv + 6t2 + -5v2 Solving for variable 't'. Remove the zero: 13tv + -6t2 + 5v2 = -13tv + 6t2 + -5v2 + 13tv + -6t2 + 5v2 Reorder the terms: 13tv + -6t2 + 5v2 = -13tv + 13tv + 6t2 + -6t2 + -5v2 + 5v2 Combine like terms: -13tv + 13tv = 0 13tv + -6t2 + 5v2 = 0 + 6t2 + -6t2 + -5v2 + 5v2 13tv + -6t2 + 5v2 = 6t2 + -6t2 + -5v2 + 5v2 Combine like terms: 6t2 + -6t2 = 0 13tv + -6t2 + 5v2 = 0 + -5v2 + 5v2 13tv + -6t2 + 5v2 = -5v2 + 5v2 Combine like terms: -5v2 + 5v2 = 0 13tv + -6t2 + 5v2 = 0 Factor a trinomial. (-3t + -1v)(2t + -5v) = 0Subproblem 1
Set the factor '(-3t + -1v)' equal to zero and attempt to solve: Simplifying -3t + -1v = 0 Solving -3t + -1v = 0 Move all terms containing t to the left, all other terms to the right. Add 'v' to each side of the equation. -3t + -1v + v = 0 + v Combine like terms: -1v + v = 0 -3t + 0 = 0 + v -3t = 0 + v Remove the zero: -3t = v Divide each side by '-3'. t = -0.3333333333v Simplifying t = -0.3333333333vSubproblem 2
Set the factor '(2t + -5v)' equal to zero and attempt to solve: Simplifying 2t + -5v = 0 Solving 2t + -5v = 0 Move all terms containing t to the left, all other terms to the right. Add '5v' to each side of the equation. 2t + -5v + 5v = 0 + 5v Combine like terms: -5v + 5v = 0 2t + 0 = 0 + 5v 2t = 0 + 5v Remove the zero: 2t = 5v Divide each side by '2'. t = 2.5v Simplifying t = 2.5vSolution
t = {-0.3333333333v, 2.5v}
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