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Simplifying X(t) = 2t + 6t2 Multiply X * t tX = 2t + 6t2 Solving tX = 2t + 6t2 Solving for variable 't'. Reorder the terms: -2t + tX + -6t2 = 2t + 6t2 + -2t + -6t2 Reorder the terms: -2t + tX + -6t2 = 2t + -2t + 6t2 + -6t2 Combine like terms: 2t + -2t = 0 -2t + tX + -6t2 = 0 + 6t2 + -6t2 -2t + tX + -6t2 = 6t2 + -6t2 Combine like terms: 6t2 + -6t2 = 0 -2t + tX + -6t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-2 + X + -6t) = 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 '(-2 + X + -6t)' equal to zero and attempt to solve: Simplifying -2 + X + -6t = 0 Solving -2 + X + -6t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + X + 2 + -6t = 0 + 2 Reorder the terms: -2 + 2 + X + -6t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + X + -6t = 0 + 2 X + -6t = 0 + 2 Combine like terms: 0 + 2 = 2 X + -6t = 2 Add '-1X' to each side of the equation. X + -1X + -6t = 2 + -1X Combine like terms: X + -1X = 0 0 + -6t = 2 + -1X -6t = 2 + -1X Divide each side by '-6'. t = -0.3333333333 + 0.1666666667X Simplifying t = -0.3333333333 + 0.1666666667XSolution
t = {0, -0.3333333333 + 0.1666666667X}
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