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Simplifying 8cos2(x) + 16cos(x) + 8 = 0 Multiply cos2 * x 8cos2x + 16cos(x) + 8 = 0 Multiply cos * x 8cos2x + 16cosx + 8 = 0 Reorder the terms: 8 + 16cosx + 8cos2x = 0 Solving 8 + 16cosx + 8cos2x = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 16cosx + -8 + 8cos2x = 0 + -8 Reorder the terms: 8 + -8 + 16cosx + 8cos2x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 16cosx + 8cos2x = 0 + -8 16cosx + 8cos2x = 0 + -8 Combine like terms: 0 + -8 = -8 16cosx + 8cos2x = -8 Reorder the terms: 8 + 16cosx + 8cos2x = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 16cosx + 8cos2x = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(1 + 2cosx + cos2x) = 0 Ignore the factor 8.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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