Sqrt(x^2+x+4)+Sqrt(x^2+x+2)=Sqrt(3x^2+3x+19)

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Solution for Sqrt(x^2+x+4)+Sqrt(x^2+x+2)=Sqrt(3x^2+3x+19) equation: 


Simplifying
Sqrt(x2 + x + 4) + Sqrt(x2 + x + 2) = Sqrt(3x2 + 3x + 19)

Reorder the terms:
qrtS(4 + x + x2) + Sqrt(x2 + x + 2) = Sqrt(3x2 + 3x + 19)
(4 * qrtS + x * qrtS + x2 * qrtS) + Sqrt(x2 + x + 2) = Sqrt(3x2 + 3x + 19)
(4qrtS + qrtxS + qrtx2S) + Sqrt(x2 + x + 2) = Sqrt(3x2 + 3x + 19)

Reorder the terms:
4qrtS + qrtxS + qrtx2S + qrtS(2 + x + x2) = Sqrt(3x2 + 3x + 19)
4qrtS + qrtxS + qrtx2S + (2 * qrtS + x * qrtS + x2 * qrtS) = Sqrt(3x2 + 3x + 19)
4qrtS + qrtxS + qrtx2S + (2qrtS + qrtxS + qrtx2S) = Sqrt(3x2 + 3x + 19)

Reorder the terms:
4qrtS + 2qrtS + qrtxS + qrtxS + qrtx2S + qrtx2S = Sqrt(3x2 + 3x + 19)

Combine like terms: 4qrtS + 2qrtS = 6qrtS
6qrtS + qrtxS + qrtxS + qrtx2S + qrtx2S = Sqrt(3x2 + 3x + 19)

Combine like terms: qrtxS + qrtxS = 2qrtxS
6qrtS + 2qrtxS + qrtx2S + qrtx2S = Sqrt(3x2 + 3x + 19)

Combine like terms: qrtx2S + qrtx2S = 2qrtx2S
6qrtS + 2qrtxS + 2qrtx2S = Sqrt(3x2 + 3x + 19)

Reorder the terms:
6qrtS + 2qrtxS + 2qrtx2S = qrtS(19 + 3x + 3x2)
6qrtS + 2qrtxS + 2qrtx2S = (19 * qrtS + 3x * qrtS + 3x2 * qrtS)
6qrtS + 2qrtxS + 2qrtx2S = (19qrtS + 3qrtxS + 3qrtx2S)

Solving
6qrtS + 2qrtxS + 2qrtx2S = 19qrtS + 3qrtxS + 3qrtx2S

Solving for variable 'q'.

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

Add '-19qrtS' to each side of the equation.
6qrtS + 2qrtxS + -19qrtS + 2qrtx2S = 19qrtS + 3qrtxS + -19qrtS + 3qrtx2S

Reorder the terms:
6qrtS + -19qrtS + 2qrtxS + 2qrtx2S = 19qrtS + 3qrtxS + -19qrtS + 3qrtx2S

Combine like terms: 6qrtS + -19qrtS = -13qrtS
-13qrtS + 2qrtxS + 2qrtx2S = 19qrtS + 3qrtxS + -19qrtS + 3qrtx2S

Reorder the terms:
-13qrtS + 2qrtxS + 2qrtx2S = 19qrtS + -19qrtS + 3qrtxS + 3qrtx2S

Combine like terms: 19qrtS + -19qrtS = 0
-13qrtS + 2qrtxS + 2qrtx2S = 0 + 3qrtxS + 3qrtx2S
-13qrtS + 2qrtxS + 2qrtx2S = 3qrtxS + 3qrtx2S

Add '-3qrtxS' to each side of the equation.
-13qrtS + 2qrtxS + -3qrtxS + 2qrtx2S = 3qrtxS + -3qrtxS + 3qrtx2S

Combine like terms: 2qrtxS + -3qrtxS = -1qrtxS
-13qrtS + -1qrtxS + 2qrtx2S = 3qrtxS + -3qrtxS + 3qrtx2S

Combine like terms: 3qrtxS + -3qrtxS = 0
-13qrtS + -1qrtxS + 2qrtx2S = 0 + 3qrtx2S
-13qrtS + -1qrtxS + 2qrtx2S = 3qrtx2S

Add '-3qrtx2S' to each side of the equation.
-13qrtS + -1qrtxS + 2qrtx2S + -3qrtx2S = 3qrtx2S + -3qrtx2S

Combine like terms: 2qrtx2S + -3qrtx2S = -1qrtx2S
-13qrtS + -1qrtxS + -1qrtx2S = 3qrtx2S + -3qrtx2S

Combine like terms: 3qrtx2S + -3qrtx2S = 0
-13qrtS + -1qrtxS + -1qrtx2S = 0

Factor out the Greatest Common Factor (GCF), '-1qrtS'.
-1qrtS(13 + x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'qrtS' equal to zero and attempt to solve:

Simplifying
qrtS = 0

Solving
qrtS = 0

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

Simplifying
qrtS = 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 '(13 + x + x2)' equal to zero and attempt to solve:

Simplifying
13 + x + x2 = 0

Solving
13 + x + x2 = 0

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

Add '-13' to each side of the equation.
13 + x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x + x2 = 0 + -13
x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
x + x2 = -13

Add '-1x' to each side of the equation.
x + -1x + x2 = -13 + -1x

Combine like terms: x + -1x = 0
0 + x2 = -13 + -1x
x2 = -13 + -1x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -13 + -1x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -13 + -1x + -1x2

Simplifying
0 = -13 + -1x + -1x2

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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