2x^2-4x-320=0

Solution for 2x^2-4x-320=0 equation:

Simplifying
2x2 + -4x + -320 = 0

Reorder the terms:
-320 + -4x + 2x2 = 0

Solving
-320 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-160 + -2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-160 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-160 + -2x + x2 = 0

Solving
-160 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + -2x + 160 + x2 = 0 + 160

Reorder the terms:
-160 + 160 + -2x + x2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + -2x + x2 = 0 + 160
-2x + x2 = 0 + 160

Combine like terms: 0 + 160 = 160
-2x + x2 = 160

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 = 160 + 1

Reorder the terms:
1 + -2x + x2 = 160 + 1

Combine like terms: 160 + 1 = 161
1 + -2x + x2 = 161

Factor a perfect square on the left side:
(x + -1)(x + -1) = 161

Calculate the square root of the right side: 12.68857754

Break this problem into two subproblems by setting 
(x + -1) equal to 12.68857754 and -12.68857754.

Subproblem 1
x + -1 = 12.68857754

Simplifying
x + -1 = 12.68857754

Reorder the terms:
-1 + x = 12.68857754

Solving
-1 + x = 12.68857754

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 = 12.68857754 + 1

Combine like terms: -1 + 1 = 0
0 + x = 12.68857754 + 1
x = 12.68857754 + 1

Combine like terms: 12.68857754 + 1 = 13.68857754
x = 13.68857754

Simplifying
x = 13.68857754

Subproblem 2
x + -1 = -12.68857754

Simplifying
x + -1 = -12.68857754

Reorder the terms:
-1 + x = -12.68857754

Solving
-1 + x = -12.68857754

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 = -12.68857754 + 1

Combine like terms: -1 + 1 = 0
0 + x = -12.68857754 + 1
x = -12.68857754 + 1

Combine like terms: -12.68857754 + 1 = -11.68857754
x = -11.68857754

Simplifying
x = -11.68857754

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.68857754, -11.68857754}
Solution
x = {13.68857754, -11.68857754}