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Simplifying 8 + -5cos(2x + -4) = 12 Reorder the terms: 8 + -5cos(-4 + 2x) = 12 8 + (-4 * -5cos + 2x * -5cos) = 12 8 + (20cos + -10cosx) = 12 Solving 8 + 20cos + -10cosx = 12 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 20cos + -8 + -10cosx = 12 + -8 Reorder the terms: 8 + -8 + 20cos + -10cosx = 12 + -8 Combine like terms: 8 + -8 = 0 0 + 20cos + -10cosx = 12 + -8 20cos + -10cosx = 12 + -8 Combine like terms: 12 + -8 = 4 20cos + -10cosx = 4 Reorder the terms: -4 + 20cos + -10cosx = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 20cos + -10cosx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 10cos + -5cosx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 10cos + -5cosx)' equal to zero and attempt to solve: Simplifying -2 + 10cos + -5cosx = 0 Solving -2 + 10cos + -5cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 10cos + 2 + -5cosx = 0 + 2 Reorder the terms: -2 + 2 + 10cos + -5cosx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 10cos + -5cosx = 0 + 2 10cos + -5cosx = 0 + 2 Combine like terms: 0 + 2 = 2 10cos + -5cosx = 2 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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