sqrt(x+3+2sqrt(x+2))+sqrt(x+3-2sqrt(x+2))=2

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Solution for sqrt(x+3+2sqrt(x+2))+sqrt(x+3-2sqrt(x+2))=2 equation: 


Simplifying
sqrt(x + 3 + 2sqrt(x + 2)) + sqrt(x + 3 + -2sqrt(x + 2)) = 2

Reorder the terms:
qrst(x + 3 + 2qrst(2 + x)) + sqrt(x + 3 + -2sqrt(x + 2)) = 2
qrst(x + 3 + (2 * 2qrst + x * 2qrst)) + sqrt(x + 3 + -2sqrt(x + 2)) = 2
qrst(x + 3 + (4qrst + 2qrstx)) + sqrt(x + 3 + -2sqrt(x + 2)) = 2

Reorder the terms:
qrst(3 + 4qrst + 2qrstx + x) + sqrt(x + 3 + -2sqrt(x + 2)) = 2
(3 * qrst + 4qrst * qrst + 2qrstx * qrst + x * qrst) + sqrt(x + 3 + -2sqrt(x + 2)) = 2

Reorder the terms:
(3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x) + sqrt(x + 3 + -2sqrt(x + 2)) = 2
(3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x) + sqrt(x + 3 + -2sqrt(x + 2)) = 2

Reorder the terms:
3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x + qrst(x + 3 + -2qrst(2 + x)) = 2
3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x + qrst(x + 3 + (2 * -2qrst + x * -2qrst)) = 2
3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x + qrst(x + 3 + (-4qrst + -2qrstx)) = 2

Reorder the terms:
3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x + qrst(3 + -4qrst + -2qrstx + x) = 2
3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x + (3 * qrst + -4qrst * qrst + -2qrstx * qrst + x * qrst) = 2

Reorder the terms:
3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x + (3qrst + qrstx + -4q2r2s2t2 + -2q2r2s2t2x) = 2
3qrst + qrstx + 4q2r2s2t2 + 2q2r2s2t2x + (3qrst + qrstx + -4q2r2s2t2 + -2q2r2s2t2x) = 2

Reorder the terms:
3qrst + 3qrst + qrstx + qrstx + 4q2r2s2t2 + -4q2r2s2t2 + 2q2r2s2t2x + -2q2r2s2t2x = 2

Combine like terms: 3qrst + 3qrst = 6qrst
6qrst + qrstx + qrstx + 4q2r2s2t2 + -4q2r2s2t2 + 2q2r2s2t2x + -2q2r2s2t2x = 2

Combine like terms: qrstx + qrstx = 2qrstx
6qrst + 2qrstx + 4q2r2s2t2 + -4q2r2s2t2 + 2q2r2s2t2x + -2q2r2s2t2x = 2

Combine like terms: 4q2r2s2t2 + -4q2r2s2t2 = 0
6qrst + 2qrstx + 0 + 2q2r2s2t2x + -2q2r2s2t2x = 2
6qrst + 2qrstx + 2q2r2s2t2x + -2q2r2s2t2x = 2

Combine like terms: 2q2r2s2t2x + -2q2r2s2t2x = 0
6qrst + 2qrstx + 0 = 2
6qrst + 2qrstx = 2

Solving
6qrst + 2qrstx = 2

Solving for variable 'q'.

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

Reorder the terms:
-2 + 6qrst + 2qrstx = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 6qrst + 2qrstx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3qrst + qrstx) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 3qrst + qrstx)' equal to zero and attempt to solve:

Simplifying
-1 + 3qrst + qrstx = 0

Solving
-1 + 3qrst + qrstx = 0

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

Add '1' to each side of the equation.
-1 + 3qrst + 1 + qrstx = 0 + 1

Reorder the terms:
-1 + 1 + 3qrst + qrstx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3qrst + qrstx = 0 + 1
3qrst + qrstx = 0 + 1

Combine like terms: 0 + 1 = 1
3qrst + qrstx = 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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