-5x^2-9x=x^2+2x-8

Solution for -5x^2-9x=x^2+2x-8 equation:

Simplifying
-5x2 + -9x = x2 + 2x + -8

Reorder the terms:
-9x + -5x2 = x2 + 2x + -8

Reorder the terms:
-9x + -5x2 = -8 + 2x + x2

Solving
-9x + -5x2 = -8 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
8 + -9x + -2x + -5x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: -9x + -2x = -11x
8 + -11x + -5x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: -5x2 + -1x2 = -6x2
8 + -11x + -6x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Reorder the terms:
8 + -11x + -6x2 = -8 + 8 + 2x + -2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
8 + -11x + -6x2 = 0 + 2x + -2x + x2 + -1x2
8 + -11x + -6x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
8 + -11x + -6x2 = 0 + x2 + -1x2
8 + -11x + -6x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -11x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.333333333 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.833333333x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.833333333x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.833333333x + x2 = 0 + 1.333333333
1.833333333x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.833333333x + x2 = 1.333333333

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = 1.333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 1.333333333 + 0.8402777775

Combine like terms: 1.333333333 + 0.8402777775 = 2.1736111105
0.8402777775 + 1.833333333x + x2 = 2.1736111105

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 2.1736111105

Calculate the square root of the right side: 1.474317168

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 1.474317168 and -1.474317168.

Subproblem 1
x + 0.9166666665 = 1.474317168

Simplifying
x + 0.9166666665 = 1.474317168

Reorder the terms:
0.9166666665 + x = 1.474317168

Solving
0.9166666665 + x = 1.474317168

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = 1.474317168 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = 1.474317168 + -0.9166666665
x = 1.474317168 + -0.9166666665

Combine like terms: 1.474317168 + -0.9166666665 = 0.5576505015
x = 0.5576505015

Simplifying
x = 0.5576505015

Subproblem 2
x + 0.9166666665 = -1.474317168

Simplifying
x + 0.9166666665 = -1.474317168

Reorder the terms:
0.9166666665 + x = -1.474317168

Solving
0.9166666665 + x = -1.474317168

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = -1.474317168 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = -1.474317168 + -0.9166666665
x = -1.474317168 + -0.9166666665

Combine like terms: -1.474317168 + -0.9166666665 = -2.3909838345
x = -2.3909838345

Simplifying
x = -2.3909838345

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5576505015, -2.3909838345}