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Simplifying sine(3x + 50) = cosine(2x + -10) Reorder the terms: eins(50 + 3x) = cosine(2x + -10) (50 * eins + 3x * eins) = cosine(2x + -10) (50eins + 3einsx) = cosine(2x + -10) Reorder the terms: 50eins + 3einsx = ceinos(-10 + 2x) 50eins + 3einsx = (-10 * ceinos + 2x * ceinos) 50eins + 3einsx = (-10ceinos + 2ceinosx) Solving 50eins + 3einsx = -10ceinos + 2ceinosx Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '10ceinos' to each side of the equation. 50eins + 10ceinos + 3einsx = -10ceinos + 10ceinos + 2ceinosx Reorder the terms: 10ceinos + 50eins + 3einsx = -10ceinos + 10ceinos + 2ceinosx Combine like terms: -10ceinos + 10ceinos = 0 10ceinos + 50eins + 3einsx = 0 + 2ceinosx 10ceinos + 50eins + 3einsx = 2ceinosx Add '-2ceinosx' to each side of the equation. 10ceinos + 50eins + -2ceinosx + 3einsx = 2ceinosx + -2ceinosx Reorder the terms: 10ceinos + -2ceinosx + 50eins + 3einsx = 2ceinosx + -2ceinosx Combine like terms: 2ceinosx + -2ceinosx = 0 10ceinos + -2ceinosx + 50eins + 3einsx = 0 Factor out the Greatest Common Factor (GCF), 'eins'. eins(10co + -2cox + 50 + 3x) = 0Subproblem 1
Set the factor 'eins' equal to zero and attempt to solve: Simplifying eins = 0 Solving eins = 0 Move all terms containing e to the left, all other terms to the right. Simplifying eins = 0 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 '(10co + -2cox + 50 + 3x)' equal to zero and attempt to solve: Simplifying 10co + -2cox + 50 + 3x = 0 Reorder the terms: 50 + 10co + -2cox + 3x = 0 Solving 50 + 10co + -2cox + 3x = 0 Move all terms containing e to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + 10co + -2cox + -50 + 3x = 0 + -50 Reorder the terms: 50 + -50 + 10co + -2cox + 3x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 10co + -2cox + 3x = 0 + -50 10co + -2cox + 3x = 0 + -50 Combine like terms: 0 + -50 = -50 10co + -2cox + 3x = -50 Add '-10co' to each side of the equation. 10co + -2cox + -10co + 3x = -50 + -10co Reorder the terms: 10co + -10co + -2cox + 3x = -50 + -10co Combine like terms: 10co + -10co = 0 0 + -2cox + 3x = -50 + -10co -2cox + 3x = -50 + -10co Add '2cox' to each side of the equation. -2cox + 2cox + 3x = -50 + -10co + 2cox Combine like terms: -2cox + 2cox = 0 0 + 3x = -50 + -10co + 2cox 3x = -50 + -10co + 2cox Add '-3x' to each side of the equation. 3x + -3x = -50 + -10co + 2cox + -3x Combine like terms: 3x + -3x = 0 0 = -50 + -10co + 2cox + -3x Simplifying 0 = -50 + -10co + 2cox + -3x 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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