2x^2-8x-4=3x+x^2

Solution for 2x^2-8x-4=3x+x^2 equation:

Simplifying
2x2 + -8x + -4 = 3x + x2

Reorder the terms:
-4 + -8x + 2x2 = 3x + x2

Solving
-4 + -8x + 2x2 = 3x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -8x + -3x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: -8x + -3x = -11x
-4 + -11x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + -11x + 1x2 = 3x + x2 + -3x + -1x2

Reorder the terms:
-4 + -11x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-4 + -11x + 1x2 = 0 + x2 + -1x2
-4 + -11x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -11x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -11x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -11x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -11x + x2 = 0 + 4
-11x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-11x + x2 = 4

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 4 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 4 + 30.25

Combine like terms: 4 + 30.25 = 34.25
30.25 + -11x + x2 = 34.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.852349955 and -5.852349955.

Subproblem 1
x + -5.5 = 5.852349955

Simplifying
x + -5.5 = 5.852349955

Reorder the terms:
-5.5 + x = 5.852349955

Solving
-5.5 + x = 5.852349955

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.852349955 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.852349955 + 5.5
x = 5.852349955 + 5.5

Combine like terms: 5.852349955 + 5.5 = 11.352349955
x = 11.352349955

Simplifying
x = 11.352349955

Subproblem 2
x + -5.5 = -5.852349955

Simplifying
x + -5.5 = -5.852349955

Reorder the terms:
-5.5 + x = -5.852349955

Solving
-5.5 + x = -5.852349955

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.852349955 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.852349955 + 5.5
x = -5.852349955 + 5.5

Combine like terms: -5.852349955 + 5.5 = -0.352349955
x = -0.352349955

Simplifying
x = -0.352349955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.352349955, -0.352349955}