sqrt(x+5)+sqrt(x+3)=2

Solution for sqrt(x+5)+sqrt(x+3)=2 equation:

Simplifying
sqrt(x + 5) + sqrt(x + 3) = 2

Reorder the terms:
qrst(5 + x) + sqrt(x + 3) = 2
(5 * qrst + x * qrst) + sqrt(x + 3) = 2
(5qrst + qrstx) + sqrt(x + 3) = 2

Reorder the terms:
5qrst + qrstx + qrst(3 + x) = 2
5qrst + qrstx + (3 * qrst + x * qrst) = 2
5qrst + qrstx + (3qrst + qrstx) = 2

Reorder the terms:
5qrst + 3qrst + qrstx + qrstx = 2

Combine like terms: 5qrst + 3qrst = 8qrst
8qrst + qrstx + qrstx = 2

Combine like terms: qrstx + qrstx = 2qrstx
8qrst + 2qrstx = 2

Solving
8qrst + 2qrstx = 2

Solving for variable 'q'.

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

Reorder the terms:
-2 + 8qrst + 2qrstx = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 8qrst + 2qrstx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4qrst + qrstx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 4qrst + qrstx)' equal to zero and attempt to solve:

Simplifying
-1 + 4qrst + qrstx = 0

Solving
-1 + 4qrst + 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 + 4qrst + 1 + qrstx = 0 + 1

Reorder the terms:
-1 + 1 + 4qrst + qrstx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4qrst + qrstx = 0 + 1
4qrst + qrstx = 0 + 1

Combine like terms: 0 + 1 = 1
4qrst + 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.