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Simplifying 20sen(5x + 7) = -5cos(5x + 7) Reorder the terms: 20ens(7 + 5x) = -5cos(5x + 7) (7 * 20ens + 5x * 20ens) = -5cos(5x + 7) (140ens + 100ensx) = -5cos(5x + 7) Reorder the terms: 140ens + 100ensx = -5cos(7 + 5x) 140ens + 100ensx = (7 * -5cos + 5x * -5cos) 140ens + 100ensx = (-35cos + -25cosx) Solving 140ens + 100ensx = -35cos + -25cosx Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Reorder the terms: 35cos + 25cosx + 140ens + 100ensx = -35cos + -25cosx + 35cos + 25cosx Reorder the terms: 35cos + 25cosx + 140ens + 100ensx = -35cos + 35cos + -25cosx + 25cosx Combine like terms: -35cos + 35cos = 0 35cos + 25cosx + 140ens + 100ensx = 0 + -25cosx + 25cosx 35cos + 25cosx + 140ens + 100ensx = -25cosx + 25cosx Combine like terms: -25cosx + 25cosx = 0 35cos + 25cosx + 140ens + 100ensx = 0 Factor out the Greatest Common Factor (GCF), '5s'. 5s(7co + 5cox + 28en + 20enx) = 0 Ignore the factor 5.Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing e to the left, all other terms to the right. Add '-1s' to each side of the equation. s + -1s = 0 + -1s Remove the zero: 0 = -1s Simplifying 0 = -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7co + 5cox + 28en + 20enx)' equal to zero and attempt to solve: Simplifying 7co + 5cox + 28en + 20enx = 0 Solving 7co + 5cox + 28en + 20enx = 0 Move all terms containing e to the left, all other terms to the right. Add '-7co' to each side of the equation. 7co + 5cox + 28en + -7co + 20enx = 0 + -7co Reorder the terms: 7co + -7co + 5cox + 28en + 20enx = 0 + -7co Combine like terms: 7co + -7co = 0 0 + 5cox + 28en + 20enx = 0 + -7co 5cox + 28en + 20enx = 0 + -7co Remove the zero: 5cox + 28en + 20enx = -7co Add '-5cox' to each side of the equation. 5cox + 28en + -5cox + 20enx = -7co + -5cox Reorder the terms: 5cox + -5cox + 28en + 20enx = -7co + -5cox Combine like terms: 5cox + -5cox = 0 0 + 28en + 20enx = -7co + -5cox 28en + 20enx = -7co + -5cox The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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