sqrt(x+1)+sqrt(4x+13)=sqrt(3x+12)

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Solution for sqrt(x+1)+sqrt(4x+13)=sqrt(3x+12) equation:


Simplifying
sqrt(x + 1) + sqrt(4x + 13) = sqrt(3x + 12)

Reorder the terms:
qrst(1 + x) + sqrt(4x + 13) = sqrt(3x + 12)
(1 * qrst + x * qrst) + sqrt(4x + 13) = sqrt(3x + 12)
(1qrst + qrstx) + sqrt(4x + 13) = sqrt(3x + 12)

Reorder the terms:
1qrst + qrstx + qrst(13 + 4x) = sqrt(3x + 12)
1qrst + qrstx + (13 * qrst + 4x * qrst) = sqrt(3x + 12)
1qrst + qrstx + (13qrst + 4qrstx) = sqrt(3x + 12)

Reorder the terms:
1qrst + 13qrst + qrstx + 4qrstx = sqrt(3x + 12)

Combine like terms: 1qrst + 13qrst = 14qrst
14qrst + qrstx + 4qrstx = sqrt(3x + 12)

Combine like terms: qrstx + 4qrstx = 5qrstx
14qrst + 5qrstx = sqrt(3x + 12)

Reorder the terms:
14qrst + 5qrstx = qrst(12 + 3x)
14qrst + 5qrstx = (12 * qrst + 3x * qrst)
14qrst + 5qrstx = (12qrst + 3qrstx)

Solving
14qrst + 5qrstx = 12qrst + 3qrstx

Solving for variable 'q'.

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

Add '-12qrst' to each side of the equation.
14qrst + -12qrst + 5qrstx = 12qrst + -12qrst + 3qrstx

Combine like terms: 14qrst + -12qrst = 2qrst
2qrst + 5qrstx = 12qrst + -12qrst + 3qrstx

Combine like terms: 12qrst + -12qrst = 0
2qrst + 5qrstx = 0 + 3qrstx
2qrst + 5qrstx = 3qrstx

Add '-3qrstx' to each side of the equation.
2qrst + 5qrstx + -3qrstx = 3qrstx + -3qrstx

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

Combine like terms: 3qrstx + -3qrstx = 0
2qrst + 2qrstx = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor 'qrst' equal to zero and attempt to solve: Simplifying qrst = 0 Solving qrst = 0 Move all terms containing q to the left, all other terms to the right. Simplifying qrst = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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