8x^2-16x-82=0

Solution for 8x^2-16x-82=0 equation:

Simplifying
8x2 + -16x + -82 = 0

Reorder the terms:
-82 + -16x + 8x2 = 0

Solving
-82 + -16x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + -8x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-41 + -8x + 4x2)' equal to zero and attempt to solve:

Simplifying
-41 + -8x + 4x2 = 0

Solving
-41 + -8x + 4x2 = 0

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

Divide each side by '4'.
-10.25 + -2x + x2 = 0

Move the constant term to the right:

Add '10.25' to each side of the equation.
-10.25 + -2x + 10.25 + x2 = 0 + 10.25

Reorder the terms:
-10.25 + 10.25 + -2x + x2 = 0 + 10.25

Combine like terms: -10.25 + 10.25 = 0.00
0.00 + -2x + x2 = 0 + 10.25
-2x + x2 = 0 + 10.25

Combine like terms: 0 + 10.25 = 10.25
-2x + x2 = 10.25

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 10.25 + 1

Reorder the terms:
1 + -2x + x2 = 10.25 + 1

Combine like terms: 10.25 + 1 = 11.25
1 + -2x + x2 = 11.25

Factor a perfect square on the left side:
(x + -1)(x + -1) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -1) equal to 3.354101966 and -3.354101966.

Subproblem 1
x + -1 = 3.354101966

Simplifying
x + -1 = 3.354101966

Reorder the terms:
-1 + x = 3.354101966

Solving
-1 + x = 3.354101966

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.354101966 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.354101966 + 1
x = 3.354101966 + 1

Combine like terms: 3.354101966 + 1 = 4.354101966
x = 4.354101966

Simplifying
x = 4.354101966

Subproblem 2
x + -1 = -3.354101966

Simplifying
x + -1 = -3.354101966

Reorder the terms:
-1 + x = -3.354101966

Solving
-1 + x = -3.354101966

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.354101966 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.354101966 + 1
x = -3.354101966 + 1

Combine like terms: -3.354101966 + 1 = -2.354101966
x = -2.354101966

Simplifying
x = -2.354101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.354101966, -2.354101966}
Solution
x = {4.354101966, -2.354101966}