x^2-[6-(4x-x^2)-(x^2+2)-5x^2]+3x^2=

Solution for x^2-[6-(4x-x^2)-(x^2+2)-5x^2]+3x^2= equation:

Simplifying
x2 + -1[6 + -1(4x + -1x2) + -1(x2 + 2) + -5x2] + 3x2 = 0
x2 + -1[6 + (4x * -1 + -1x2 * -1) + -1(x2 + 2) + -5x2] + 3x2 = 0
x2 + -1[6 + (-4x + 1x2) + -1(x2 + 2) + -5x2] + 3x2 = 0

Reorder the terms:
x2 + -1[6 + -4x + 1x2 + -1(2 + x2) + -5x2] + 3x2 = 0
x2 + -1[6 + -4x + 1x2 + (2 * -1 + x2 * -1) + -5x2] + 3x2 = 0
x2 + -1[6 + -4x + 1x2 + (-2 + -1x2) + -5x2] + 3x2 = 0

Reorder the terms:
x2 + -1[6 + -2 + -4x + 1x2 + -1x2 + -5x2] + 3x2 = 0

Combine like terms: 6 + -2 = 4
x2 + -1[4 + -4x + 1x2 + -1x2 + -5x2] + 3x2 = 0

Combine like terms: 1x2 + -1x2 = 0
x2 + -1[4 + -4x + 0 + -5x2] + 3x2 = 0
x2 + -1[4 + -4x + -5x2] + 3x2 = 0
x2 + [4 * -1 + -4x * -1 + -5x2 * -1] + 3x2 = 0
x2 + [-4 + 4x + 5x2] + 3x2 = 0

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

Combine like terms: x2 + 5x2 = 6x2
-4 + 4x + 6x2 + 3x2 = 0

Combine like terms: 6x2 + 3x2 = 9x2
-4 + 4x + 9x2 = 0

Solving
-4 + 4x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.4444444444 + 0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + 0.4444444444x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + 0.4444444444x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + 0.4444444444x + x2 = 0 + 0.4444444444
0.4444444444x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
0.4444444444x + x2 = 0.4444444444

The x term is 0.4444444444x.  Take half its coefficient (0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
0.4444444444x + 0.04938271604 + x2 = 0.4444444444 + 0.04938271604

Reorder the terms:
0.04938271604 + 0.4444444444x + x2 = 0.4444444444 + 0.04938271604

Combine like terms: 0.4444444444 + 0.04938271604 = 0.49382716044
0.04938271604 + 0.4444444444x + x2 = 0.49382716044

Factor a perfect square on the left side:
(x + 0.2222222222)(x + 0.2222222222) = 0.49382716044

Calculate the square root of the right side: 0.702728369

Break this problem into two subproblems by setting 
(x + 0.2222222222) equal to 0.702728369 and -0.702728369.

Subproblem 1
x + 0.2222222222 = 0.702728369

Simplifying
x + 0.2222222222 = 0.702728369

Reorder the terms:
0.2222222222 + x = 0.702728369

Solving
0.2222222222 + x = 0.702728369

Solving for variable 'x'.

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

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = 0.702728369 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = 0.702728369 + -0.2222222222
x = 0.702728369 + -0.2222222222

Combine like terms: 0.702728369 + -0.2222222222 = 0.4805061468
x = 0.4805061468

Simplifying
x = 0.4805061468

Subproblem 2
x + 0.2222222222 = -0.702728369

Simplifying
x + 0.2222222222 = -0.702728369

Reorder the terms:
0.2222222222 + x = -0.702728369

Solving
0.2222222222 + x = -0.702728369

Solving for variable 'x'.

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

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = -0.702728369 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = -0.702728369 + -0.2222222222
x = -0.702728369 + -0.2222222222

Combine like terms: -0.702728369 + -0.2222222222 = -0.9249505912
x = -0.9249505912

Simplifying
x = -0.9249505912

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4805061468, -0.9249505912}