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Simplifying 3 = 8cos(2x + 1) + 7 Reorder the terms: 3 = 8cos(1 + 2x) + 7 3 = (1 * 8cos + 2x * 8cos) + 7 3 = (8cos + 16cosx) + 7 Reorder the terms: 3 = 7 + 8cos + 16cosx Solving 3 = 7 + 8cos + 16cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8cos' to each side of the equation. 3 + -8cos = 7 + 8cos + -8cos + 16cosx Combine like terms: 8cos + -8cos = 0 3 + -8cos = 7 + 0 + 16cosx 3 + -8cos = 7 + 16cosx Add '-16cosx' to each side of the equation. 3 + -8cos + -16cosx = 7 + 16cosx + -16cosx Combine like terms: 16cosx + -16cosx = 0 3 + -8cos + -16cosx = 7 + 0 3 + -8cos + -16cosx = 7 Add '-3' to each side of the equation. 3 + -8cos + -3 + -16cosx = 7 + -3 Reorder the terms: 3 + -3 + -8cos + -16cosx = 7 + -3 Combine like terms: 3 + -3 = 0 0 + -8cos + -16cosx = 7 + -3 -8cos + -16cosx = 7 + -3 Combine like terms: 7 + -3 = 4 -8cos + -16cosx = 4 Reorder the terms: -4 + -8cos + -16cosx = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -8cos + -16cosx = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(1 + 2cos + 4cosx) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(1 + 2cos + 4cosx)' equal to zero and attempt to solve: Simplifying 1 + 2cos + 4cosx = 0 Solving 1 + 2cos + 4cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2cos + -1 + 4cosx = 0 + -1 Reorder the terms: 1 + -1 + 2cos + 4cosx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2cos + 4cosx = 0 + -1 2cos + 4cosx = 0 + -1 Combine like terms: 0 + -1 = -1 2cos + 4cosx = -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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