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Simplifying v(t) = 37t + -2t2 Multiply v * t tv = 37t + -2t2 Solving tv = 37t + -2t2 Solving for variable 't'. Reorder the terms: -37t + tv + 2t2 = 37t + -2t2 + -37t + 2t2 Reorder the terms: -37t + tv + 2t2 = 37t + -37t + -2t2 + 2t2 Combine like terms: 37t + -37t = 0 -37t + tv + 2t2 = 0 + -2t2 + 2t2 -37t + tv + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -37t + tv + 2t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-37 + v + 2t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-37 + v + 2t)' equal to zero and attempt to solve: Simplifying -37 + v + 2t = 0 Reorder the terms: -37 + 2t + v = 0 Solving -37 + 2t + v = 0 Move all terms containing t to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 2t + 37 + v = 0 + 37 Reorder the terms: -37 + 37 + 2t + v = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 2t + v = 0 + 37 2t + v = 0 + 37 Combine like terms: 0 + 37 = 37 2t + v = 37 Add '-1v' to each side of the equation. 2t + v + -1v = 37 + -1v Combine like terms: v + -1v = 0 2t + 0 = 37 + -1v 2t = 37 + -1v Divide each side by '2'. t = 18.5 + -0.5v Simplifying t = 18.5 + -0.5vSolution
t = {0, 18.5 + -0.5v}
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