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Simplifying 0 = cos2x + 4cosx + 3 Reorder the terms: 0 = 3 + 4cosx + cos2x Solving 0 = 3 + 4cosx + cos2x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4cosx' to each side of the equation. 0 + -4cosx = 3 + 4cosx + -4cosx + cos2x Remove the zero: -4cosx = 3 + 4cosx + -4cosx + cos2x Combine like terms: 4cosx + -4cosx = 0 -4cosx = 3 + 0 + cos2x -4cosx = 3 + cos2x Add '-1cos2x' to each side of the equation. -4cosx + -1cos2x = 3 + cos2x + -1cos2x Combine like terms: cos2x + -1cos2x = 0 -4cosx + -1cos2x = 3 + 0 -4cosx + -1cos2x = 3 Reorder the terms: -3 + -4cosx + -1cos2x = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -4cosx + -1cos2x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 4cosx + cos2x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 4cosx + cos2x)' equal to zero and attempt to solve: Simplifying 3 + 4cosx + cos2x = 0 Solving 3 + 4cosx + cos2x = 0 Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 4cosx + -3 + cos2x = 0 + -3 Reorder the terms: 3 + -3 + 4cosx + cos2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4cosx + cos2x = 0 + -3 4cosx + cos2x = 0 + -3 Combine like terms: 0 + -3 = -3 4cosx + cos2x = -3 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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