sqrt(x+42)+sqrt(x+10)=8

Solution for sqrt(x+42)+sqrt(x+10)=8 equation:

Simplifying
sqrt(x + 42) + sqrt(x + 10) = 8

Reorder the terms:
qrst(42 + x) + sqrt(x + 10) = 8
(42 * qrst + x * qrst) + sqrt(x + 10) = 8
(42qrst + qrstx) + sqrt(x + 10) = 8

Reorder the terms:
42qrst + qrstx + qrst(10 + x) = 8
42qrst + qrstx + (10 * qrst + x * qrst) = 8
42qrst + qrstx + (10qrst + qrstx) = 8

Reorder the terms:
42qrst + 10qrst + qrstx + qrstx = 8

Combine like terms: 42qrst + 10qrst = 52qrst
52qrst + qrstx + qrstx = 8

Combine like terms: qrstx + qrstx = 2qrstx
52qrst + 2qrstx = 8

Solving
52qrst + 2qrstx = 8

Solving for variable 'q'.

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

Reorder the terms:
-8 + 52qrst + 2qrstx = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 52qrst + 2qrstx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 26qrst + qrstx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 26qrst + qrstx)' equal to zero and attempt to solve:

Simplifying
-4 + 26qrst + qrstx = 0

Solving
-4 + 26qrst + qrstx = 0

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

Add '4' to each side of the equation.
-4 + 26qrst + 4 + qrstx = 0 + 4

Reorder the terms:
-4 + 4 + 26qrst + qrstx = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 26qrst + qrstx = 0 + 4
26qrst + qrstx = 0 + 4

Combine like terms: 0 + 4 = 4
26qrst + qrstx = 4

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.