2cos^2x-1+4cosx=-3

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Solution for 2cos^2x-1+4cosx=-3 equation:


Simplifying
2cos2x + -1 + 4cosx = -3

Reorder the terms:
-1 + 4cosx + 2cos2x = -3

Solving
-1 + 4cosx + 2cos2x = -3

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 4cosx + 1 + 2cos2x = -3 + 1

Reorder the terms:
-1 + 1 + 4cosx + 2cos2x = -3 + 1

Combine like terms: -1 + 1 = 0
0 + 4cosx + 2cos2x = -3 + 1
4cosx + 2cos2x = -3 + 1

Combine like terms: -3 + 1 = -2
4cosx + 2cos2x = -2

Reorder the terms:
2 + 4cosx + 2cos2x = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 4cosx + 2cos2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2cosx + cos2x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 2cosx + cos2x)' equal to zero and attempt to solve: Simplifying 1 + 2cosx + cos2x = 0 Solving 1 + 2cosx + cos2x = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2cosx + -1 + cos2x = 0 + -1 Reorder the terms: 1 + -1 + 2cosx + cos2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2cosx + cos2x = 0 + -1 2cosx + cos2x = 0 + -1 Combine like terms: 0 + -1 = -1 2cosx + cos2x = -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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