sqrt(x+1)+sqrt(x+2)+sqrt(x+3)+sqrt(x+4)=4

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Solution for sqrt(x+1)+sqrt(x+2)+sqrt(x+3)+sqrt(x+4)=4 equation:


Simplifying
sqrt(x + 1) + sqrt(x + 2) + sqrt(x + 3) + sqrt(x + 4) = 4

Reorder the terms:
qrst(1 + x) + sqrt(x + 2) + sqrt(x + 3) + sqrt(x + 4) = 4
(1 * qrst + x * qrst) + sqrt(x + 2) + sqrt(x + 3) + sqrt(x + 4) = 4
(1qrst + qrstx) + sqrt(x + 2) + sqrt(x + 3) + sqrt(x + 4) = 4

Reorder the terms:
1qrst + qrstx + qrst(2 + x) + sqrt(x + 3) + sqrt(x + 4) = 4
1qrst + qrstx + (2 * qrst + x * qrst) + sqrt(x + 3) + sqrt(x + 4) = 4
1qrst + qrstx + (2qrst + qrstx) + sqrt(x + 3) + sqrt(x + 4) = 4

Reorder the terms:
1qrst + qrstx + 2qrst + qrstx + qrst(3 + x) + sqrt(x + 4) = 4
1qrst + qrstx + 2qrst + qrstx + (3 * qrst + x * qrst) + sqrt(x + 4) = 4
1qrst + qrstx + 2qrst + qrstx + (3qrst + qrstx) + sqrt(x + 4) = 4

Reorder the terms:
1qrst + qrstx + 2qrst + qrstx + 3qrst + qrstx + qrst(4 + x) = 4
1qrst + qrstx + 2qrst + qrstx + 3qrst + qrstx + (4 * qrst + x * qrst) = 4
1qrst + qrstx + 2qrst + qrstx + 3qrst + qrstx + (4qrst + qrstx) = 4

Reorder the terms:
1qrst + 2qrst + 3qrst + 4qrst + qrstx + qrstx + qrstx + qrstx = 4

Combine like terms: 1qrst + 2qrst = 3qrst
3qrst + 3qrst + 4qrst + qrstx + qrstx + qrstx + qrstx = 4

Combine like terms: 3qrst + 3qrst = 6qrst
6qrst + 4qrst + qrstx + qrstx + qrstx + qrstx = 4

Combine like terms: 6qrst + 4qrst = 10qrst
10qrst + qrstx + qrstx + qrstx + qrstx = 4

Combine like terms: qrstx + qrstx = 2qrstx
10qrst + 2qrstx + qrstx + qrstx = 4

Combine like terms: 2qrstx + qrstx = 3qrstx
10qrst + 3qrstx + qrstx = 4

Combine like terms: 3qrstx + qrstx = 4qrstx
10qrst + 4qrstx = 4

Solving
10qrst + 4qrstx = 4

Solving for variable 'q'.

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

Reorder the terms:
-4 + 10qrst + 4qrstx = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 10qrst + 4qrstx = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + 5qrst + 2qrstx)' equal to zero and attempt to solve: Simplifying -2 + 5qrst + 2qrstx = 0 Solving -2 + 5qrst + 2qrstx = 0 Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 5qrst + 2 + 2qrstx = 0 + 2 Reorder the terms: -2 + 2 + 5qrst + 2qrstx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5qrst + 2qrstx = 0 + 2 5qrst + 2qrstx = 0 + 2 Combine like terms: 0 + 2 = 2 5qrst + 2qrstx = 2 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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