x^2+(x^2-4x+5)-3x+5(x^2-4x+5)-11=0

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Solution for x^2+(x^2-4x+5)-3x+5(x^2-4x+5)-11=0 equation: 


Simplifying
x2 + (x2 + -4x + 5) + -3x + 5(x2 + -4x + 5) + -11 = 0

Reorder the terms:
x2 + (5 + -4x + x2) + -3x + 5(x2 + -4x + 5) + -11 = 0

Remove parenthesis around (5 + -4x + x2)
x2 + 5 + -4x + x2 + -3x + 5(x2 + -4x + 5) + -11 = 0

Reorder the terms:
x2 + 5 + -4x + x2 + -3x + 5(5 + -4x + x2) + -11 = 0
x2 + 5 + -4x + x2 + -3x + (5 * 5 + -4x * 5 + x2 * 5) + -11 = 0
x2 + 5 + -4x + x2 + -3x + (25 + -20x + 5x2) + -11 = 0

Reorder the terms:
5 + 25 + -11 + -4x + -3x + -20x + x2 + x2 + 5x2 = 0

Combine like terms: 5 + 25 = 30
30 + -11 + -4x + -3x + -20x + x2 + x2 + 5x2 = 0

Combine like terms: 30 + -11 = 19
19 + -4x + -3x + -20x + x2 + x2 + 5x2 = 0

Combine like terms: -4x + -3x = -7x
19 + -7x + -20x + x2 + x2 + 5x2 = 0

Combine like terms: -7x + -20x = -27x
19 + -27x + x2 + x2 + 5x2 = 0

Combine like terms: x2 + x2 = 2x2
19 + -27x + 2x2 + 5x2 = 0

Combine like terms: 2x2 + 5x2 = 7x2
19 + -27x + 7x2 = 0

Solving
19 + -27x + 7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
2.714285714 + -3.857142857x + x2 = 0

Move the constant term to the right:

Add '-2.714285714' to each side of the equation.
2.714285714 + -3.857142857x + -2.714285714 + x2 = 0 + -2.714285714

Reorder the terms:
2.714285714 + -2.714285714 + -3.857142857x + x2 = 0 + -2.714285714

Combine like terms: 2.714285714 + -2.714285714 = 0.000000000
0.000000000 + -3.857142857x + x2 = 0 + -2.714285714
-3.857142857x + x2 = 0 + -2.714285714

Combine like terms: 0 + -2.714285714 = -2.714285714
-3.857142857x + x2 = -2.714285714

The x term is -3.857142857x.  Take half its coefficient (-1.928571429).
Square it (3.719387757) and add it to both sides.

Add '3.719387757' to each side of the equation.
-3.857142857x + 3.719387757 + x2 = -2.714285714 + 3.719387757

Reorder the terms:
3.719387757 + -3.857142857x + x2 = -2.714285714 + 3.719387757

Combine like terms: -2.714285714 + 3.719387757 = 1.005102043
3.719387757 + -3.857142857x + x2 = 1.005102043

Factor a perfect square on the left side:
(x + -1.928571429)(x + -1.928571429) = 1.005102043

Calculate the square root of the right side: 1.002547776

Break this problem into two subproblems by setting 
(x + -1.928571429) equal to 1.002547776 and -1.002547776.


Subproblem 1
x + -1.928571429 = 1.002547776

Simplifying
x + -1.928571429 = 1.002547776

Reorder the terms:
-1.928571429 + x = 1.002547776

Solving
-1.928571429 + x = 1.002547776

Solving for variable 'x'.

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

Add '1.928571429' to each side of the equation.
-1.928571429 + 1.928571429 + x = 1.002547776 + 1.928571429

Combine like terms: -1.928571429 + 1.928571429 = 0.000000000
0.000000000 + x = 1.002547776 + 1.928571429
x = 1.002547776 + 1.928571429

Combine like terms: 1.002547776 + 1.928571429 = 2.931119205
x = 2.931119205

Simplifying
x = 2.931119205


Subproblem 2
x + -1.928571429 = -1.002547776

Simplifying
x + -1.928571429 = -1.002547776

Reorder the terms:
-1.928571429 + x = -1.002547776

Solving
-1.928571429 + x = -1.002547776

Solving for variable 'x'.

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

Add '1.928571429' to each side of the equation.
-1.928571429 + 1.928571429 + x = -1.002547776 + 1.928571429

Combine like terms: -1.928571429 + 1.928571429 = 0.000000000
0.000000000 + x = -1.002547776 + 1.928571429
x = -1.002547776 + 1.928571429

Combine like terms: -1.002547776 + 1.928571429 = 0.926023653
x = 0.926023653

Simplifying
x = 0.926023653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.931119205, 0.926023653}

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