2x^2-172x+68=0

Solution for 2x^2-172x+68=0 equation:

Simplifying
2x2 + -172x + 68 = 0

Reorder the terms:
68 + -172x + 2x2 = 0

Solving
68 + -172x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(34 + -86x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(34 + -86x + x2)' equal to zero and attempt to solve:

Simplifying
34 + -86x + x2 = 0

Solving
34 + -86x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -86x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -86x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -86x + x2 = 0 + -34
-86x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-86x + x2 = -34

The x term is -86x.  Take half its coefficient (-43).
Square it (1849) and add it to both sides.

Add '1849' to each side of the equation.
-86x + 1849 + x2 = -34 + 1849

Reorder the terms:
1849 + -86x + x2 = -34 + 1849

Combine like terms: -34 + 1849 = 1815
1849 + -86x + x2 = 1815

Factor a perfect square on the left side:
(x + -43)(x + -43) = 1815

Calculate the square root of the right side: 42.602816808

Break this problem into two subproblems by setting 
(x + -43) equal to 42.602816808 and -42.602816808.

Subproblem 1
x + -43 = 42.602816808

Simplifying
x + -43 = 42.602816808

Reorder the terms:
-43 + x = 42.602816808

Solving
-43 + x = 42.602816808

Solving for variable 'x'.

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

Add '43' to each side of the equation.
-43 + 43 + x = 42.602816808 + 43

Combine like terms: -43 + 43 = 0
0 + x = 42.602816808 + 43
x = 42.602816808 + 43

Combine like terms: 42.602816808 + 43 = 85.602816808
x = 85.602816808

Simplifying
x = 85.602816808

Subproblem 2
x + -43 = -42.602816808

Simplifying
x + -43 = -42.602816808

Reorder the terms:
-43 + x = -42.602816808

Solving
-43 + x = -42.602816808

Solving for variable 'x'.

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

Add '43' to each side of the equation.
-43 + 43 + x = -42.602816808 + 43

Combine like terms: -43 + 43 = 0
0 + x = -42.602816808 + 43
x = -42.602816808 + 43

Combine like terms: -42.602816808 + 43 = 0.397183192
x = 0.397183192

Simplifying
x = 0.397183192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {85.602816808, 0.397183192}
Solution
x = {85.602816808, 0.397183192}