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Simplifying x(t) = 12t + -6t2 Multiply x * t tx = 12t + -6t2 Solving tx = 12t + -6t2 Solving for variable 't'. Reorder the terms: -12t + tx + 6t2 = 12t + -6t2 + -12t + 6t2 Reorder the terms: -12t + tx + 6t2 = 12t + -12t + -6t2 + 6t2 Combine like terms: 12t + -12t = 0 -12t + tx + 6t2 = 0 + -6t2 + 6t2 -12t + tx + 6t2 = -6t2 + 6t2 Combine like terms: -6t2 + 6t2 = 0 -12t + tx + 6t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-12 + 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 '(-12 + x + 6t)' equal to zero and attempt to solve: Simplifying -12 + x + 6t = 0 Reorder the terms: -12 + 6t + x = 0 Solving -12 + 6t + x = 0 Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 6t + 12 + x = 0 + 12 Reorder the terms: -12 + 12 + 6t + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 6t + x = 0 + 12 6t + x = 0 + 12 Combine like terms: 0 + 12 = 12 6t + x = 12 Add '-1x' to each side of the equation. 6t + x + -1x = 12 + -1x Combine like terms: x + -1x = 0 6t + 0 = 12 + -1x 6t = 12 + -1x Divide each side by '6'. t = 2 + -0.1666666667x Simplifying t = 2 + -0.1666666667xSolution
t = {0, 2 + -0.1666666667x}
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