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Simplifying 2cos(4x) + -1 = 16cos4(x) + -16cos2(x) + 1 Remove parenthesis around (4x) 2cos * 4x + -1 = 16cos4(x) + -16cos2(x) + 1 Reorder the terms for easier multiplication: 2 * 4cos * x + -1 = 16cos4(x) + -16cos2(x) + 1 Multiply 2 * 4 8cos * x + -1 = 16cos4(x) + -16cos2(x) + 1 Multiply cos * x 8cosx + -1 = 16cos4(x) + -16cos2(x) + 1 Reorder the terms: -1 + 8cosx = 16cos4(x) + -16cos2(x) + 1 Multiply cos4 * x -1 + 8cosx = 16cos4x + -16cos2(x) + 1 Multiply cos2 * x -1 + 8cosx = 16cos4x + -16cos2x + 1 Reorder the terms: -1 + 8cosx = 1 + -16cos2x + 16cos4x Solving -1 + 8cosx = 1 + -16cos2x + 16cos4x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '16cos2x' to each side of the equation. -1 + 8cosx + 16cos2x = 1 + -16cos2x + 16cos2x + 16cos4x Combine like terms: -16cos2x + 16cos2x = 0 -1 + 8cosx + 16cos2x = 1 + 0 + 16cos4x -1 + 8cosx + 16cos2x = 1 + 16cos4x Add '-16cos4x' to each side of the equation. -1 + 8cosx + 16cos2x + -16cos4x = 1 + 16cos4x + -16cos4x Combine like terms: 16cos4x + -16cos4x = 0 -1 + 8cosx + 16cos2x + -16cos4x = 1 + 0 -1 + 8cosx + 16cos2x + -16cos4x = 1 Add '1' to each side of the equation. -1 + 8cosx + 16cos2x + 1 + -16cos4x = 1 + 1 Reorder the terms: -1 + 1 + 8cosx + 16cos2x + -16cos4x = 1 + 1 Combine like terms: -1 + 1 = 0 0 + 8cosx + 16cos2x + -16cos4x = 1 + 1 8cosx + 16cos2x + -16cos4x = 1 + 1 Combine like terms: 1 + 1 = 2 8cosx + 16cos2x + -16cos4x = 2 Reorder the terms: -2 + 8cosx + 16cos2x + -16cos4x = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 8cosx + 16cos2x + -16cos4x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 4cosx + 8cos2x + -8cos4x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 4cosx + 8cos2x + -8cos4x)' equal to zero and attempt to solve: Simplifying -1 + 4cosx + 8cos2x + -8cos4x = 0 Solving -1 + 4cosx + 8cos2x + -8cos4x = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 4cosx + 8cos2x + 1 + -8cos4x = 0 + 1 Reorder the terms: -1 + 1 + 4cosx + 8cos2x + -8cos4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4cosx + 8cos2x + -8cos4x = 0 + 1 4cosx + 8cos2x + -8cos4x = 0 + 1 Combine like terms: 0 + 1 = 1 4cosx + 8cos2x + -8cos4x = 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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