0=x^2+8x-6

Solution for 0=x^2+8x-6 equation:

Simplifying
0 = x2 + 8x + -6

Reorder the terms:
0 = -6 + 8x + x2

Solving
0 = -6 + 8x + x2

Solving for variable 'x'.

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

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

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

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 8x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 8x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 8x + x2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
8x + x2 = 6

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 6 + 16

Reorder the terms:
16 + 8x + x2 = 6 + 16

Combine like terms: 6 + 16 = 22
16 + 8x + x2 = 22

Factor a perfect square on the left side:
(x + 4)(x + 4) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + 4) equal to 4.69041576 and -4.69041576.

Subproblem 1
x + 4 = 4.69041576

Simplifying
x + 4 = 4.69041576

Reorder the terms:
4 + x = 4.69041576

Solving
4 + x = 4.69041576

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.69041576 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.69041576 + -4
x = 4.69041576 + -4

Combine like terms: 4.69041576 + -4 = 0.69041576
x = 0.69041576

Simplifying
x = 0.69041576

Subproblem 2
x + 4 = -4.69041576

Simplifying
x + 4 = -4.69041576

Reorder the terms:
4 + x = -4.69041576

Solving
4 + x = -4.69041576

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.69041576 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.69041576 + -4
x = -4.69041576 + -4

Combine like terms: -4.69041576 + -4 = -8.69041576
x = -8.69041576

Simplifying
x = -8.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.69041576, -8.69041576}