x^2-x^2-8x^2-x+12=0

Solution for x^2-x^2-8x^2-x+12=0 equation:

Simplifying
x2 + -1x2 + -8x2 + -1x + 12 = 0

Reorder the terms:
12 + -1x + x2 + -1x2 + -8x2 = 0

Combine like terms: x2 + -1x2 = 0
12 + -1x + 0 + -8x2 = 0
12 + -1x + -8x2 = 0

Solving
12 + -1x + -8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.5 + 0.125x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.125x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.125x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.125x + x2 = 0 + 1.5
0.125x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.125x + x2 = 1.5

The x term is 0.125x.  Take half its coefficient (0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
0.125x + 0.00390625 + x2 = 1.5 + 0.00390625

Reorder the terms:
0.00390625 + 0.125x + x2 = 1.5 + 0.00390625

Combine like terms: 1.5 + 0.00390625 = 1.50390625
0.00390625 + 0.125x + x2 = 1.50390625

Factor a perfect square on the left side:
(x + 0.0625)(x + 0.0625) = 1.50390625

Calculate the square root of the right side: 1.226338554

Break this problem into two subproblems by setting 
(x + 0.0625) equal to 1.226338554 and -1.226338554.

Subproblem 1
x + 0.0625 = 1.226338554

Simplifying
x + 0.0625 = 1.226338554

Reorder the terms:
0.0625 + x = 1.226338554

Solving
0.0625 + x = 1.226338554

Solving for variable 'x'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + x = 1.226338554 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + x = 1.226338554 + -0.0625
x = 1.226338554 + -0.0625

Combine like terms: 1.226338554 + -0.0625 = 1.163838554
x = 1.163838554

Simplifying
x = 1.163838554

Subproblem 2
x + 0.0625 = -1.226338554

Simplifying
x + 0.0625 = -1.226338554

Reorder the terms:
0.0625 + x = -1.226338554

Solving
0.0625 + x = -1.226338554

Solving for variable 'x'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + x = -1.226338554 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + x = -1.226338554 + -0.0625
x = -1.226338554 + -0.0625

Combine like terms: -1.226338554 + -0.0625 = -1.288838554
x = -1.288838554

Simplifying
x = -1.288838554

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.163838554, -1.288838554}