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

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


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

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

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

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

Remove parenthesis around (2cosx)
4cos2x + 2cosx + 2qrst * 2cosx + sqrt(2) = 0

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

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

Multiply qrst * cosx
4cos2x + 2cosx + 4coqrs2tx + sqrt(2) = 0

Reorder the terms for easier multiplication:
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 + qrt) = 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 + qrt)' equal to zero and attempt to solve:

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

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

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

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

Add '-1qrt' to each side of the equation.
2coqrstx + 2cosx + cox + qrt + -1qrt = 0 + -1qrt

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

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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