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Simplifying 2cos2(2x) + 3cos(2x) + -2 = 0 Remove parenthesis around (2x) 2cos2 * 2x + 3cos(2x) + -2 = 0 Reorder the terms for easier multiplication: 2 * 2cos2 * x + 3cos(2x) + -2 = 0 Multiply 2 * 2 4cos2 * x + 3cos(2x) + -2 = 0 Multiply cos2 * x 4cos2x + 3cos(2x) + -2 = 0 Remove parenthesis around (2x) 4cos2x + 3cos * 2x + -2 = 0 Reorder the terms for easier multiplication: 4cos2x + 3 * 2cos * x + -2 = 0 Multiply 3 * 2 4cos2x + 6cos * x + -2 = 0 Multiply cos * x 4cos2x + 6cosx + -2 = 0 Reorder the terms: -2 + 6cosx + 4cos2x = 0 Solving -2 + 6cosx + 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 + 6cosx + 2 + 4cos2x = 0 + 2 Reorder the terms: -2 + 2 + 6cosx + 4cos2x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6cosx + 4cos2x = 0 + 2 6cosx + 4cos2x = 0 + 2 Combine like terms: 0 + 2 = 2 6cosx + 4cos2x = 2 Reorder the terms: -2 + 6cosx + 4cos2x = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 6cosx + 4cos2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 3cosx + 2cos2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 3cosx + 2cos2x)' equal to zero and attempt to solve: Simplifying -1 + 3cosx + 2cos2x = 0 Solving -1 + 3cosx + 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 + 3cosx + 1 + 2cos2x = 0 + 1 Reorder the terms: -1 + 1 + 3cosx + 2cos2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3cosx + 2cos2x = 0 + 1 3cosx + 2cos2x = 0 + 1 Combine like terms: 0 + 1 = 1 3cosx + 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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