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Simplifying 3cos2x + 6cosx + 3 = 0 Reorder the terms: 3 + 6cosx + 3cos2x = 0 Solving 3 + 6cosx + 3cos2x = 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 + 6cosx + -3 + 3cos2x = 0 + -3 Reorder the terms: 3 + -3 + 6cosx + 3cos2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6cosx + 3cos2x = 0 + -3 6cosx + 3cos2x = 0 + -3 Combine like terms: 0 + -3 = -3 6cosx + 3cos2x = -3 Reorder the terms: 3 + 6cosx + 3cos2x = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 6cosx + 3cos2x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 2cosx + cos2x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 2cosx + cos2x)' equal to zero and attempt to solve: Simplifying 1 + 2cosx + cos2x = 0 Solving 1 + 2cosx + cos2x = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2cosx + -1 + cos2x = 0 + -1 Reorder the terms: 1 + -1 + 2cosx + cos2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2cosx + cos2x = 0 + -1 2cosx + cos2x = 0 + -1 Combine like terms: 0 + -1 = -1 2cosx + cos2x = -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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