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Simplifying 2cos3(3x) + 2cos2(3x) + -3cos(3x) + -3 = 0 Remove parenthesis around (3x) 2cos3 * 3x + 2cos2(3x) + -3cos(3x) + -3 = 0 Reorder the terms for easier multiplication: 2 * 3cos3 * x + 2cos2(3x) + -3cos(3x) + -3 = 0 Multiply 2 * 3 6cos3 * x + 2cos2(3x) + -3cos(3x) + -3 = 0 Multiply cos3 * x 6cos3x + 2cos2(3x) + -3cos(3x) + -3 = 0 Remove parenthesis around (3x) 6cos3x + 2cos2 * 3x + -3cos(3x) + -3 = 0 Reorder the terms for easier multiplication: 6cos3x + 2 * 3cos2 * x + -3cos(3x) + -3 = 0 Multiply 2 * 3 6cos3x + 6cos2 * x + -3cos(3x) + -3 = 0 Multiply cos2 * x 6cos3x + 6cos2x + -3cos(3x) + -3 = 0 Remove parenthesis around (3x) 6cos3x + 6cos2x + -3cos * 3x + -3 = 0 Reorder the terms for easier multiplication: 6cos3x + 6cos2x + -3 * 3cos * x + -3 = 0 Multiply -3 * 3 6cos3x + 6cos2x + -9cos * x + -3 = 0 Multiply cos * x 6cos3x + 6cos2x + -9cosx + -3 = 0 Reorder the terms: -3 + -9cosx + 6cos2x + 6cos3x = 0 Solving -3 + -9cosx + 6cos2x + 6cos3x = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -9cosx + 6cos2x + 3 + 6cos3x = 0 + 3 Reorder the terms: -3 + 3 + -9cosx + 6cos2x + 6cos3x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9cosx + 6cos2x + 6cos3x = 0 + 3 -9cosx + 6cos2x + 6cos3x = 0 + 3 Combine like terms: 0 + 3 = 3 -9cosx + 6cos2x + 6cos3x = 3 Reorder the terms: -3 + -9cosx + 6cos2x + 6cos3x = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -9cosx + 6cos2x + 6cos3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -3cosx + 2cos2x + 2cos3x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -3cosx + 2cos2x + 2cos3x)' equal to zero and attempt to solve: Simplifying -1 + -3cosx + 2cos2x + 2cos3x = 0 Solving -1 + -3cosx + 2cos2x + 2cos3x = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -3cosx + 2cos2x + 1 + 2cos3x = 0 + 1 Reorder the terms: -1 + 1 + -3cosx + 2cos2x + 2cos3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3cosx + 2cos2x + 2cos3x = 0 + 1 -3cosx + 2cos2x + 2cos3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3cosx + 2cos2x + 2cos3x = 1 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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