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Simplifying 6cos2x + 12cosx + 6 = 0 Reorder the terms: 6 + 12cosx + 6cos2x = 0 Solving 6 + 12cosx + 6cos2x = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 12cosx + -6 + 6cos2x = 0 + -6 Reorder the terms: 6 + -6 + 12cosx + 6cos2x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 12cosx + 6cos2x = 0 + -6 12cosx + 6cos2x = 0 + -6 Combine like terms: 0 + -6 = -6 12cosx + 6cos2x = -6 Reorder the terms: 6 + 12cosx + 6cos2x = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 12cosx + 6cos2x = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(1 + 2cosx + cos2x) = 0 Ignore the factor 6.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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