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Simplifying 6cos2x + 2cosx + -4 = 0 Reorder the terms: -4 + 2cosx + 6cos2x = 0 Solving -4 + 2cosx + 6cos2x = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 2cosx + 4 + 6cos2x = 0 + 4 Reorder the terms: -4 + 4 + 2cosx + 6cos2x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2cosx + 6cos2x = 0 + 4 2cosx + 6cos2x = 0 + 4 Combine like terms: 0 + 4 = 4 2cosx + 6cos2x = 4 Reorder the terms: -4 + 2cosx + 6cos2x = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 2cosx + 6cos2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + cosx + 3cos2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + cosx + 3cos2x)' equal to zero and attempt to solve: Simplifying -2 + cosx + 3cos2x = 0 Solving -2 + cosx + 3cos2x = 0 Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + cosx + 2 + 3cos2x = 0 + 2 Reorder the terms: -2 + 2 + cosx + 3cos2x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + cosx + 3cos2x = 0 + 2 cosx + 3cos2x = 0 + 2 Combine like terms: 0 + 2 = 2 cosx + 3cos2x = 2 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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