x^2-8x-68=0

Solution for x^2-8x-68=0 equation:

Simplifying
x2 + -8x + -68 = 0

Reorder the terms:
-68 + -8x + x2 = 0

Solving
-68 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + -8x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + -8x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -8x + x2 = 0 + 68
-8x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
-8x + x2 = 68

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 = 68 + 16

Reorder the terms:
16 + -8x + x2 = 68 + 16

Combine like terms: 68 + 16 = 84
16 + -8x + x2 = 84

Factor a perfect square on the left side:
(x + -4)(x + -4) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + -4) equal to 9.16515139 and -9.16515139.

Subproblem 1
x + -4 = 9.16515139

Simplifying
x + -4 = 9.16515139

Reorder the terms:
-4 + x = 9.16515139

Solving
-4 + x = 9.16515139

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 = 9.16515139 + 4

Combine like terms: -4 + 4 = 0
0 + x = 9.16515139 + 4
x = 9.16515139 + 4

Combine like terms: 9.16515139 + 4 = 13.16515139
x = 13.16515139

Simplifying
x = 13.16515139

Subproblem 2
x + -4 = -9.16515139

Simplifying
x + -4 = -9.16515139

Reorder the terms:
-4 + x = -9.16515139

Solving
-4 + x = -9.16515139

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 = -9.16515139 + 4

Combine like terms: -4 + 4 = 0
0 + x = -9.16515139 + 4
x = -9.16515139 + 4

Combine like terms: -9.16515139 + 4 = -5.16515139
x = -5.16515139

Simplifying
x = -5.16515139

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.16515139, -5.16515139}