6-8x-8x-4x^2-x^2=11

Solution for 6-8x-8x-4x^2-x^2=11 equation:

Simplifying
6 + -8x + -8x + -4x2 + -1x2 = 11

Combine like terms: -8x + -8x = -16x
6 + -16x + -4x2 + -1x2 = 11

Combine like terms: -4x2 + -1x2 = -5x2
6 + -16x + -5x2 = 11

Solving
6 + -16x + -5x2 = 11

Solving for variable 'x'.

Reorder the terms:
6 + -11 + -16x + -5x2 = 11 + -11

Combine like terms: 6 + -11 = -5
-5 + -16x + -5x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-5 + -16x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 16x + 5x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 16x + 5x2)' equal to zero and attempt to solve:

Simplifying
5 + 16x + 5x2 = 0

Solving
5 + 16x + 5x2 = 0

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

Divide each side by '5'.
1 + 3.2x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3.2x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3.2x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3.2x + x2 = 0 + -1
3.2x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3.2x + x2 = -1

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = -1 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = -1 + 2.56

Combine like terms: -1 + 2.56 = 1.56
2.56 + 3.2x + x2 = 1.56

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 1.56

Calculate the square root of the right side: 1.2489996

Break this problem into two subproblems by setting 
(x + 1.6) equal to 1.2489996 and -1.2489996.

Subproblem 1
x + 1.6 = 1.2489996

Simplifying
x + 1.6 = 1.2489996

Reorder the terms:
1.6 + x = 1.2489996

Solving
1.6 + x = 1.2489996

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = 1.2489996 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = 1.2489996 + -1.6
x = 1.2489996 + -1.6

Combine like terms: 1.2489996 + -1.6 = -0.3510004
x = -0.3510004

Simplifying
x = -0.3510004

Subproblem 2
x + 1.6 = -1.2489996

Simplifying
x + 1.6 = -1.2489996

Reorder the terms:
1.6 + x = -1.2489996

Solving
1.6 + x = -1.2489996

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = -1.2489996 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = -1.2489996 + -1.6
x = -1.2489996 + -1.6

Combine like terms: -1.2489996 + -1.6 = -2.8489996
x = -2.8489996

Simplifying
x = -2.8489996

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.3510004, -2.8489996}
Solution
x = {-0.3510004, -2.8489996}