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Simplifying 12cos2(x) + 8cos(x) + -20 = 0 Multiply cos2 * x 12cos2x + 8cos(x) + -20 = 0 Multiply cos * x 12cos2x + 8cosx + -20 = 0 Reorder the terms: -20 + 8cosx + 12cos2x = 0 Solving -20 + 8cosx + 12cos2x = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 8cosx + 20 + 12cos2x = 0 + 20 Reorder the terms: -20 + 20 + 8cosx + 12cos2x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 8cosx + 12cos2x = 0 + 20 8cosx + 12cos2x = 0 + 20 Combine like terms: 0 + 20 = 20 8cosx + 12cos2x = 20 Reorder the terms: -20 + 8cosx + 12cos2x = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 8cosx + 12cos2x = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 2cosx + 3cos2x) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 2cosx + 3cos2x)' equal to zero and attempt to solve: Simplifying -5 + 2cosx + 3cos2x = 0 Solving -5 + 2cosx + 3cos2x = 0 Move all terms containing c to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 2cosx + 5 + 3cos2x = 0 + 5 Reorder the terms: -5 + 5 + 2cosx + 3cos2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2cosx + 3cos2x = 0 + 5 2cosx + 3cos2x = 0 + 5 Combine like terms: 0 + 5 = 5 2cosx + 3cos2x = 5 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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