sqrt(x+34)+sqrt(x+14)=10

Solution for sqrt(x+34)+sqrt(x+14)=10 equation:

Simplifying
sqrt(x + 34) + sqrt(x + 14) = 10

Reorder the terms:
qrst(34 + x) + sqrt(x + 14) = 10
(34 * qrst + x * qrst) + sqrt(x + 14) = 10
(34qrst + qrstx) + sqrt(x + 14) = 10

Reorder the terms:
34qrst + qrstx + qrst(14 + x) = 10
34qrst + qrstx + (14 * qrst + x * qrst) = 10
34qrst + qrstx + (14qrst + qrstx) = 10

Reorder the terms:
34qrst + 14qrst + qrstx + qrstx = 10

Combine like terms: 34qrst + 14qrst = 48qrst
48qrst + qrstx + qrstx = 10

Combine like terms: qrstx + qrstx = 2qrstx
48qrst + 2qrstx = 10

Solving
48qrst + 2qrstx = 10

Solving for variable 'q'.

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

Reorder the terms:
-10 + 48qrst + 2qrstx = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 48qrst + 2qrstx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 24qrst + qrstx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 24qrst + qrstx)' equal to zero and attempt to solve:

Simplifying
-5 + 24qrst + qrstx = 0

Solving
-5 + 24qrst + qrstx = 0

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

Add '5' to each side of the equation.
-5 + 24qrst + 5 + qrstx = 0 + 5

Reorder the terms:
-5 + 5 + 24qrst + qrstx = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 24qrst + qrstx = 0 + 5
24qrst + qrstx = 0 + 5

Combine like terms: 0 + 5 = 5
24qrst + qrstx = 5

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.