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Simplifying 1 = 10cos(x + 1) + -4 Reorder the terms: 1 = 10cos(1 + x) + -4 1 = (1 * 10cos + x * 10cos) + -4 1 = (10cos + 10cosx) + -4 Reorder the terms: 1 = -4 + 10cos + 10cosx Solving 1 = -4 + 10cos + 10cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10cos' to each side of the equation. 1 + -10cos = -4 + 10cos + -10cos + 10cosx Combine like terms: 10cos + -10cos = 0 1 + -10cos = -4 + 0 + 10cosx 1 + -10cos = -4 + 10cosx Add '-10cosx' to each side of the equation. 1 + -10cos + -10cosx = -4 + 10cosx + -10cosx Combine like terms: 10cosx + -10cosx = 0 1 + -10cos + -10cosx = -4 + 0 1 + -10cos + -10cosx = -4 Add '-1' to each side of the equation. 1 + -10cos + -1 + -10cosx = -4 + -1 Reorder the terms: 1 + -1 + -10cos + -10cosx = -4 + -1 Combine like terms: 1 + -1 = 0 0 + -10cos + -10cosx = -4 + -1 -10cos + -10cosx = -4 + -1 Combine like terms: -4 + -1 = -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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