X^2+2Sqrt(x^2-3x+11)=3x+4

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Solution for X^2+2Sqrt(x^2-3x+11)=3x+4 equation: 


Simplifying
X2 + 2Sqrt(x2 + -3x + 11) = 3x + 4

Reorder the terms:
X2 + 2qrtS(11 + -3x + x2) = 3x + 4
X2 + (11 * 2qrtS + -3x * 2qrtS + x2 * 2qrtS) = 3x + 4
X2 + (22qrtS + -6qrtxS + 2qrtx2S) = 3x + 4

Reorder the terms:
X2 + 22qrtS + -6qrtxS + 2qrtx2S = 4 + 3x

Solving
X2 + 22qrtS + -6qrtxS + 2qrtx2S = 4 + 3x

Solving for variable 'X'.

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

Add '-22qrtS' to each side of the equation.
X2 + 22qrtS + -6qrtxS + -22qrtS + 2qrtx2S = 4 + -22qrtS + 3x

Reorder the terms:
X2 + 22qrtS + -22qrtS + -6qrtxS + 2qrtx2S = 4 + -22qrtS + 3x

Combine like terms: 22qrtS + -22qrtS = 0
X2 + 0 + -6qrtxS + 2qrtx2S = 4 + -22qrtS + 3x
X2 + -6qrtxS + 2qrtx2S = 4 + -22qrtS + 3x

Add '6qrtxS' to each side of the equation.
X2 + -6qrtxS + 6qrtxS + 2qrtx2S = 4 + -22qrtS + 6qrtxS + 3x

Combine like terms: -6qrtxS + 6qrtxS = 0
X2 + 0 + 2qrtx2S = 4 + -22qrtS + 6qrtxS + 3x
X2 + 2qrtx2S = 4 + -22qrtS + 6qrtxS + 3x

Add '-2qrtx2S' to each side of the equation.
X2 + 2qrtx2S + -2qrtx2S = 4 + -22qrtS + 6qrtxS + -2qrtx2S + 3x

Combine like terms: 2qrtx2S + -2qrtx2S = 0
X2 + 0 = 4 + -22qrtS + 6qrtxS + -2qrtx2S + 3x
X2 = 4 + -22qrtS + 6qrtxS + -2qrtx2S + 3x

Simplifying
X2 = 4 + -22qrtS + 6qrtxS + -2qrtx2S + 3x

Reorder the terms:
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 4 + -22qrtS + 6qrtxS + -2qrtx2S + 3x + -4 + 22qrtS + -6qrtxS + 2qrtx2S + -3x

Reorder the terms:
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 4 + -4 + -22qrtS + 22qrtS + 6qrtxS + -6qrtxS + -2qrtx2S + 2qrtx2S + 3x + -3x

Combine like terms: 4 + -4 = 0
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 0 + -22qrtS + 22qrtS + 6qrtxS + -6qrtxS + -2qrtx2S + 2qrtx2S + 3x + -3x
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = -22qrtS + 22qrtS + 6qrtxS + -6qrtxS + -2qrtx2S + 2qrtx2S + 3x + -3x

Combine like terms: -22qrtS + 22qrtS = 0
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 0 + 6qrtxS + -6qrtxS + -2qrtx2S + 2qrtx2S + 3x + -3x
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 6qrtxS + -6qrtxS + -2qrtx2S + 2qrtx2S + 3x + -3x

Combine like terms: 6qrtxS + -6qrtxS = 0
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 0 + -2qrtx2S + 2qrtx2S + 3x + -3x
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = -2qrtx2S + 2qrtx2S + 3x + -3x

Combine like terms: -2qrtx2S + 2qrtx2S = 0
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 0 + 3x + -3x
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + X2 + 22qrtS + -6qrtxS + 2qrtx2S + -3x = 0

The solution to this equation could not be determined.

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