2x^2-x-68=0

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

Simplifying
2x2 + -1x + -68 = 0

Reorder the terms:
-68 + -1x + 2x2 = 0

Solving
-68 + -1x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-34 + -0.5x + x2 = 0

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -0.5x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -0.5x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -0.5x + x2 = 0 + 34
-0.5x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-0.5x + x2 = 34

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 34 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 34 + 0.0625

Combine like terms: 34 + 0.0625 = 34.0625
0.0625 + -0.5x + x2 = 34.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 34.0625

Calculate the square root of the right side: 5.836308765

Break this problem into two subproblems by setting 
(x + -0.25) equal to 5.836308765 and -5.836308765.

Subproblem 1
x + -0.25 = 5.836308765

Simplifying
x + -0.25 = 5.836308765

Reorder the terms:
-0.25 + x = 5.836308765

Solving
-0.25 + x = 5.836308765

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 5.836308765 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 5.836308765 + 0.25
x = 5.836308765 + 0.25

Combine like terms: 5.836308765 + 0.25 = 6.086308765
x = 6.086308765

Simplifying
x = 6.086308765

Subproblem 2
x + -0.25 = -5.836308765

Simplifying
x + -0.25 = -5.836308765

Reorder the terms:
-0.25 + x = -5.836308765

Solving
-0.25 + x = -5.836308765

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -5.836308765 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -5.836308765 + 0.25
x = -5.836308765 + 0.25

Combine like terms: -5.836308765 + 0.25 = -5.586308765
x = -5.586308765

Simplifying
x = -5.586308765

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.086308765, -5.586308765}