4cos^2x-2(1-sqrt(2))cosx-sqrt(2)=0

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Solution for 4cos^2x-2(1-sqrt(2))cosx-sqrt(2)=0 equation: 


Simplifying
4cos2x + -2(1 + -1sqrt(2)) * cosx + -1sqrt(2) = 0

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

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

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

Reorder the terms:
4cos2x + (4coqrs2tx + -2cosx) + -1sqrt(2) = 0
4cos2x + (4coqrs2tx + -2cosx) + -1sqrt(2) = 0

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

Multiply -1 * 2
4cos2x + 4coqrs2tx + -2cosx + -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 + -1cox + 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 + -1cox + 2cosx + -1qrt)' equal to zero and attempt to solve:

Simplifying
2coqrstx + -1cox + 2cosx + -1qrt = 0

Reorder the terms:
2coqrstx + 2cosx + -1cox + -1qrt = 0

Solving
2coqrstx + 2cosx + -1cox + -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 + -1cox + -1qrt + qrt = 0 + qrt

Combine like terms: -1qrt + qrt = 0
2coqrstx + 2cosx + -1cox + 0 = 0 + qrt
2coqrstx + 2cosx + -1cox = 0 + qrt
Remove the zero:
2coqrstx + 2cosx + -1cox = 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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