2x^2-24x-68=0

Solution for 2x^2-24x-68=0 equation:

Simplifying
2x2 + -24x + -68 = 0

Reorder the terms:
-68 + -24x + 2x2 = 0

Solving
-68 + -24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-34 + -12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-34 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-34 + -12x + x2 = 0

Solving
-34 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -12x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -12x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -12x + x2 = 0 + 34
-12x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-12x + x2 = 34

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 34 + 36

Reorder the terms:
36 + -12x + x2 = 34 + 36

Combine like terms: 34 + 36 = 70
36 + -12x + x2 = 70

Factor a perfect square on the left side:
(x + -6)(x + -6) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + -6) equal to 8.366600265 and -8.366600265.

Subproblem 1
x + -6 = 8.366600265

Simplifying
x + -6 = 8.366600265

Reorder the terms:
-6 + x = 8.366600265

Solving
-6 + x = 8.366600265

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 8.366600265 + 6

Combine like terms: -6 + 6 = 0
0 + x = 8.366600265 + 6
x = 8.366600265 + 6

Combine like terms: 8.366600265 + 6 = 14.366600265
x = 14.366600265

Simplifying
x = 14.366600265

Subproblem 2
x + -6 = -8.366600265

Simplifying
x + -6 = -8.366600265

Reorder the terms:
-6 + x = -8.366600265

Solving
-6 + x = -8.366600265

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -8.366600265 + 6

Combine like terms: -6 + 6 = 0
0 + x = -8.366600265 + 6
x = -8.366600265 + 6

Combine like terms: -8.366600265 + 6 = -2.366600265
x = -2.366600265

Simplifying
x = -2.366600265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.366600265, -2.366600265}
Solution
x = {14.366600265, -2.366600265}