4cos^2(x)+2cos(x)-2sqrt(2)cos(x)-sqrt(2)=0

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Solution for 4cos^2(x)+2cos(x)-2sqrt(2)cos(x)-sqrt(2)=0 equation:


Simplifying
4cos2(x) + 2cos(x) + -2sqrt(2) * cos(x) + -1sqrt(2) = 0

Multiply cos2 * x
4cos2x + 2cos(x) + -2sqrt(2) * cos(x) + -1sqrt(2) = 0

Multiply cos * x
4cos2x + 2cosx + -2sqrt(2) * cos(x) + -1sqrt(2) = 0

Reorder the terms for easier multiplication:
4cos2x + 2cosx + -2 * 2qrst * cos * x + -1sqrt(2) = 0

Multiply -2 * 2
4cos2x + 2cosx + -4qrst * cos * x + -1sqrt(2) = 0

Multiply qrst * cos
4cos2x + 2cosx + -4coqrs2t * x + -1sqrt(2) = 0

Multiply coqrs2t * x
4cos2x + 2cosx + -4coqrs2tx + -1sqrt(2) = 0

Reorder the terms for easier multiplication:
4cos2x + 2cosx + -4coqrs2tx + -1 * 2qrst = 0

Multiply -1 * 2
4cos2x + 2cosx + -4coqrs2tx + -2qrst = 0

Reorder the terms:
-4coqrs2tx + 2cosx + 4cos2x + -2qrst = 0

Solving
-4coqrs2tx + 2cosx + 4cos2x + -2qrst = 0

Solving for variable 'c'.

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

Add '2qrst' to each side of the equation.
-4coqrs2tx + 2cosx + 4cos2x + -2qrst + 2qrst = 0 + 2qrst

Combine like terms: -2qrst + 2qrst = 0
-4coqrs2tx + 2cosx + 4cos2x + 0 = 0 + 2qrst
-4coqrs2tx + 2cosx + 4cos2x = 0 + 2qrst
Remove the zero:
-4coqrs2tx + 2cosx + 4cos2x = 2qrst

Combine like terms: 2qrst + -2qrst = 0
-4coqrs2tx + 2cosx + 4cos2x + -2qrst = 0

Factor out the Greatest Common Factor (GCF), '2s'.
2s(-2coqrstx + cox + 2cosx + -1qrt) = 0

Ignore the factor 2.

Subproblem 1

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