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Simplifying 4cos2x + 2cosx + -2 = 0 Reorder the terms: -2 + 2cosx + 4cos2x = 0 Solving -2 + 2cosx + 4cos2x = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2cosx + 2 + 4cos2x = 0 + 2 Reorder the terms: -2 + 2 + 2cosx + 4cos2x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2cosx + 4cos2x = 0 + 2 2cosx + 4cos2x = 0 + 2 Combine like terms: 0 + 2 = 2 2cosx + 4cos2x = 2 Reorder the terms: -2 + 2cosx + 4cos2x = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 2cosx + 4cos2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + cosx + 2cos2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + cosx + 2cos2x)' equal to zero and attempt to solve: Simplifying -1 + cosx + 2cos2x = 0 Solving -1 + cosx + 2cos2x = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + cosx + 1 + 2cos2x = 0 + 1 Reorder the terms: -1 + 1 + cosx + 2cos2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + cosx + 2cos2x = 0 + 1 cosx + 2cos2x = 0 + 1 Combine like terms: 0 + 1 = 1 cosx + 2cos2x = 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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