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Simplifying cos2x + -1(a + 1) * cosx + 3a + -6 = 0 Reorder the terms: cos2x + -1(1 + a) * cosx + 3a + -6 = 0 Reorder the terms for easier multiplication: cos2x + -1cosx(1 + a) + 3a + -6 = 0 cos2x + (1 * -1cosx + a * -1cosx) + 3a + -6 = 0 Reorder the terms: cos2x + (-1acosx + -1cosx) + 3a + -6 = 0 cos2x + (-1acosx + -1cosx) + 3a + -6 = 0 Reorder the terms: -6 + 3a + -1acosx + -1cosx + cos2x = 0 Solving -6 + 3a + -1acosx + -1cosx + cos2x = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 3a + -1acosx + -1cosx + 6 + cos2x = 0 + 6 Reorder the terms: -6 + 6 + 3a + -1acosx + -1cosx + cos2x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3a + -1acosx + -1cosx + cos2x = 0 + 6 3a + -1acosx + -1cosx + cos2x = 0 + 6 Combine like terms: 0 + 6 = 6 3a + -1acosx + -1cosx + cos2x = 6 Add 'cosx' to each side of the equation. 3a + -1acosx + -1cosx + cosx + cos2x = 6 + cosx Combine like terms: -1cosx + cosx = 0 3a + -1acosx + 0 + cos2x = 6 + cosx 3a + -1acosx + cos2x = 6 + cosx Add '-1cos2x' to each side of the equation. 3a + -1acosx + cos2x + -1cos2x = 6 + cosx + -1cos2x Combine like terms: cos2x + -1cos2x = 0 3a + -1acosx + 0 = 6 + cosx + -1cos2x 3a + -1acosx = 6 + cosx + -1cos2x Reorder the terms: -6 + 3a + -1acosx + -1cosx + cos2x = 6 + cosx + -1cos2x + -6 + -1cosx + cos2x Reorder the terms: -6 + 3a + -1acosx + -1cosx + cos2x = 6 + -6 + cosx + -1cosx + -1cos2x + cos2x Combine like terms: 6 + -6 = 0 -6 + 3a + -1acosx + -1cosx + cos2x = 0 + cosx + -1cosx + -1cos2x + cos2x -6 + 3a + -1acosx + -1cosx + cos2x = cosx + -1cosx + -1cos2x + cos2x Combine like terms: cosx + -1cosx = 0 -6 + 3a + -1acosx + -1cosx + cos2x = 0 + -1cos2x + cos2x -6 + 3a + -1acosx + -1cosx + cos2x = -1cos2x + cos2x Combine like terms: -1cos2x + cos2x = 0 -6 + 3a + -1acosx + -1cosx + cos2x = 0 The solution to this equation could not be determined.
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