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Simplifying 10cos(x + 1) + -4 = 1 Reorder the terms: 10cos(1 + x) + -4 = 1 (1 * 10cos + x * 10cos) + -4 = 1 (10cos + 10cosx) + -4 = 1 Reorder the terms: -4 + 10cos + 10cosx = 1 Solving -4 + 10cos + 10cosx = 1 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 10cos + 4 + 10cosx = 1 + 4 Reorder the terms: -4 + 4 + 10cos + 10cosx = 1 + 4 Combine like terms: -4 + 4 = 0 0 + 10cos + 10cosx = 1 + 4 10cos + 10cosx = 1 + 4 Combine like terms: 1 + 4 = 5 10cos + 10cosx = 5 Reorder the terms: -5 + 10cos + 10cosx = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 10cos + 10cosx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + 2cos + 2cosx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + 2cos + 2cosx)' equal to zero and attempt to solve: Simplifying -1 + 2cos + 2cosx = 0 Solving -1 + 2cos + 2cosx = 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 + 2cosx = 0 + 1 Reorder the terms: -1 + 1 + 2cos + 2cosx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2cos + 2cosx = 0 + 1 2cos + 2cosx = 0 + 1 Combine like terms: 0 + 1 = 1 2cos + 2cosx = 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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