2x-2=8x^2

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

Simplifying
2x + -2 = 8x2

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

Solving
-2 + 2x = 8x2

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + x + -4x2)' equal to zero and attempt to solve:

Simplifying
-1 + x + -4x2 = 0

Solving
-1 + x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -0.25x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.25x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.25x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.25x + x2 = 0 + -0.25
-0.25x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.25x + x2 = -0.25

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.
-0.25x + 0.25 + x2 = -0.25 + 0.25

Reorder the terms:
0.25 + -0.25x + x2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -0.25x + x2 = 0.00

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.00 and 0.00.

Subproblem 1
x + 0.5 = 0.00

Simplifying
x + 0.5 = 0.00

Reorder the terms:
0.5 + x = 0.00

Solving
0.5 + x = 0.00

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 = 0.00 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.00 + -0.5
x = 0.00 + -0.5

Combine like terms: 0.00 + -0.5 = -0.5
x = -0.5

Simplifying
x = -0.5

Subproblem 2
x + 0.5 = 0.00

Simplifying
x + 0.5 = 0.00

Reorder the terms:
0.5 + x = 0.00

Solving
0.5 + x = 0.00

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 = 0.00 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.00 + -0.5
x = 0.00 + -0.5

Combine like terms: 0.00 + -0.5 = -0.5
x = -0.5

Simplifying
x = -0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -0.5}
Solution
x = {-0.5, -0.5}