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Simplifying 5 = -5cos(18x + 6) Reorder the terms: 5 = -5cos(6 + 18x) 5 = (6 * -5cos + 18x * -5cos) 5 = (-30cos + -90cosx) Solving 5 = -30cos + -90cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '30cos' to each side of the equation. 5 + 30cos = -30cos + 30cos + -90cosx Combine like terms: -30cos + 30cos = 0 5 + 30cos = 0 + -90cosx 5 + 30cos = -90cosx Add '90cosx' to each side of the equation. 5 + 30cos + 90cosx = -90cosx + 90cosx Combine like terms: -90cosx + 90cosx = 0 5 + 30cos + 90cosx = 0 Add '-5' to each side of the equation. 5 + 30cos + -5 + 90cosx = 0 + -5 Reorder the terms: 5 + -5 + 30cos + 90cosx = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 30cos + 90cosx = 0 + -5 30cos + 90cosx = 0 + -5 Combine like terms: 0 + -5 = -5 30cos + 90cosx = -5 Reorder the terms: 5 + 30cos + 90cosx = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 30cos + 90cosx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 6cos + 18cosx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 6cos + 18cosx)' equal to zero and attempt to solve: Simplifying 1 + 6cos + 18cosx = 0 Solving 1 + 6cos + 18cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 6cos + -1 + 18cosx = 0 + -1 Reorder the terms: 1 + -1 + 6cos + 18cosx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6cos + 18cosx = 0 + -1 6cos + 18cosx = 0 + -1 Combine like terms: 0 + -1 = -1 6cos + 18cosx = -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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