8x^2-19=2x^2-x

Solution for 8x^2-19=2x^2-x equation:

Simplifying
8x2 + -19 = 2x2 + -1x

Reorder the terms:
-19 + 8x2 = 2x2 + -1x

Reorder the terms:
-19 + 8x2 = -1x + 2x2

Solving
-19 + 8x2 = -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-19 + x + 8x2 + -2x2 = -1x + 2x2 + x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
-19 + x + 6x2 = -1x + 2x2 + x + -2x2

Reorder the terms:
-19 + x + 6x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-19 + x + 6x2 = 0 + 2x2 + -2x2
-19 + x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-19 + x + 6x2 = 0

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

Divide each side by '6'.
-3.166666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '3.166666667' to each side of the equation.
-3.166666667 + 0.1666666667x + 3.166666667 + x2 = 0 + 3.166666667

Reorder the terms:
-3.166666667 + 3.166666667 + 0.1666666667x + x2 = 0 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + 0.1666666667x + x2 = 0 + 3.166666667
0.1666666667x + x2 = 0 + 3.166666667

Combine like terms: 0 + 3.166666667 = 3.166666667
0.1666666667x + x2 = 3.166666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = 3.166666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = 3.166666667 + 0.25

Combine like terms: 3.166666667 + 0.25 = 3.416666667
0.25 + 0.1666666667x + x2 = 3.416666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.416666667

Calculate the square root of the right side: 1.848422751

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.848422751 and -1.848422751.

Subproblem 1
x + 0.5 = 1.848422751

Simplifying
x + 0.5 = 1.848422751

Reorder the terms:
0.5 + x = 1.848422751

Solving
0.5 + x = 1.848422751

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.848422751 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.848422751 + -0.5
x = 1.848422751 + -0.5

Combine like terms: 1.848422751 + -0.5 = 1.348422751
x = 1.348422751

Simplifying
x = 1.348422751

Subproblem 2
x + 0.5 = -1.848422751

Simplifying
x + 0.5 = -1.848422751

Reorder the terms:
0.5 + x = -1.848422751

Solving
0.5 + x = -1.848422751

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.848422751 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.848422751 + -0.5
x = -1.848422751 + -0.5

Combine like terms: -1.848422751 + -0.5 = -2.348422751
x = -2.348422751

Simplifying
x = -2.348422751

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.348422751, -2.348422751}