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Simplifying x(t) = u(7t + sqrt(3)) * u(-7t + sqrt(3)) Multiply x * t tx = u(7t + sqrt(3)) * u(-7t + sqrt(3)) Reorder the terms for easier multiplication: tx = u(7t + 3qrst) * u(-7t + sqrt(3)) Reorder the terms: tx = u(3qrst + 7t) * u(-7t + sqrt(3)) Reorder the terms for easier multiplication: tx = u(3qrst + 7t) * u(-7t + 3qrst) Reorder the terms: tx = u(3qrst + 7t) * u(3qrst + -7t) Reorder the terms for easier multiplication: tx = u * u(3qrst + 7t)(3qrst + -7t) Multiply u * u tx = u2(3qrst + 7t)(3qrst + -7t) Multiply (3qrst + 7t) * (3qrst + -7t) tx = u2(3qrst * (3qrst + -7t) + 7t * (3qrst + -7t)) tx = u2((3qrst * 3qrst + -7t * 3qrst) + 7t * (3qrst + -7t)) Reorder the terms: tx = u2((-21qrst2 + 9q2r2s2t2) + 7t * (3qrst + -7t)) tx = u2((-21qrst2 + 9q2r2s2t2) + 7t * (3qrst + -7t)) tx = u2(-21qrst2 + 9q2r2s2t2 + (3qrst * 7t + -7t * 7t)) tx = u2(-21qrst2 + 9q2r2s2t2 + (21qrst2 + -49t2)) Reorder the terms: tx = u2(-21qrst2 + 21qrst2 + 9q2r2s2t2 + -49t2) Combine like terms: -21qrst2 + 21qrst2 = 0 tx = u2(0 + 9q2r2s2t2 + -49t2) tx = u2(9q2r2s2t2 + -49t2) tx = (9q2r2s2t2 * u2 + -49t2 * u2) tx = (9q2r2s2t2u2 + -49t2u2) Solving tx = 9q2r2s2t2u2 + -49t2u2 Solving for variable 't'. Reorder the terms: -9q2r2s2t2u2 + tx + 49t2u2 = 9q2r2s2t2u2 + -49t2u2 + -9q2r2s2t2u2 + 49t2u2 Reorder the terms: -9q2r2s2t2u2 + tx + 49t2u2 = 9q2r2s2t2u2 + -9q2r2s2t2u2 + -49t2u2 + 49t2u2 Combine like terms: 9q2r2s2t2u2 + -9q2r2s2t2u2 = 0 -9q2r2s2t2u2 + tx + 49t2u2 = 0 + -49t2u2 + 49t2u2 -9q2r2s2t2u2 + tx + 49t2u2 = -49t2u2 + 49t2u2 Combine like terms: -49t2u2 + 49t2u2 = 0 -9q2r2s2t2u2 + tx + 49t2u2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-9q2r2s2tu2 + x + 49tu2) = 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 '(-9q2r2s2tu2 + x + 49tu2)' equal to zero and attempt to solve: Simplifying -9q2r2s2tu2 + x + 49tu2 = 0 Reorder the terms: -9q2r2s2tu2 + 49tu2 + x = 0 Solving -9q2r2s2tu2 + 49tu2 + x = 0 Move all terms containing t to the left, all other terms to the right. Add '-1x' to each side of the equation. -9q2r2s2tu2 + 49tu2 + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 -9q2r2s2tu2 + 49tu2 + 0 = 0 + -1x -9q2r2s2tu2 + 49tu2 = 0 + -1x Remove the zero: -9q2r2s2tu2 + 49tu2 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
t = {0}
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