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Simplifying 0 = 120cosx + 100cos2x + -100sin2x Solving 0 = 120cosx + 100cos2x + -100in2sx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-120cosx' to each side of the equation. 0 + -120cosx = 120cosx + 100cos2x + -120cosx + -100in2sx Remove the zero: -120cosx = 120cosx + 100cos2x + -120cosx + -100in2sx Reorder the terms: -120cosx = 120cosx + -120cosx + 100cos2x + -100in2sx Combine like terms: 120cosx + -120cosx = 0 -120cosx = 0 + 100cos2x + -100in2sx -120cosx = 100cos2x + -100in2sx Add '-100cos2x' to each side of the equation. -120cosx + -100cos2x = 100cos2x + -100cos2x + -100in2sx Combine like terms: 100cos2x + -100cos2x = 0 -120cosx + -100cos2x = 0 + -100in2sx -120cosx + -100cos2x = -100in2sx Combine like terms: -100in2sx + 100in2sx = 0 -120cosx + -100cos2x + 100in2sx = 0 Factor out the Greatest Common Factor (GCF), '20sx'. 20sx(-6co + -5cos + 5in2) = 0 Ignore the factor 20.Subproblem 1
Set the factor 'sx' equal to zero and attempt to solve: Simplifying sx = 0 Solving sx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1sx' to each side of the equation. sx + -1sx = 0 + -1sx Remove the zero: 0 = -1sx Simplifying 0 = -1sx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-6co + -5cos + 5in2)' equal to zero and attempt to solve: Simplifying -6co + -5cos + 5in2 = 0 Solving -6co + -5cos + 5in2 = 0 Move all terms containing c to the left, all other terms to the right. Add '-5in2' to each side of the equation. -6co + -5cos + 5in2 + -5in2 = 0 + -5in2 Combine like terms: 5in2 + -5in2 = 0 -6co + -5cos + 0 = 0 + -5in2 -6co + -5cos = 0 + -5in2 Remove the zero: -6co + -5cos = -5in2 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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