0=2(x^2-2x-520)

Solution for 0=2(x^2-2x-520) equation:

Simplifying
0 = 2(x2 + -2x + -520)

Reorder the terms:
0 = 2(-520 + -2x + x2)
0 = (-520 * 2 + -2x * 2 + x2 * 2)
0 = (-1040 + -4x + 2x2)

Solving
0 = -1040 + -4x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 1040 = 1040
1040 + 4x + -2x2 = -1040 + -4x + 2x2 + 1040 + 4x + -2x2

Reorder the terms:
1040 + 4x + -2x2 = -1040 + 1040 + -4x + 4x + 2x2 + -2x2

Combine like terms: -1040 + 1040 = 0
1040 + 4x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2
1040 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
1040 + 4x + -2x2 = 0 + 2x2 + -2x2
1040 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1040 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(520 + 2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(520 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
520 + 2x + -1x2 = 0

Solving
520 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-520 + -2x + x2 = 0

Move the constant term to the right:

Add '520' to each side of the equation.
-520 + -2x + 520 + x2 = 0 + 520

Reorder the terms:
-520 + 520 + -2x + x2 = 0 + 520

Combine like terms: -520 + 520 = 0
0 + -2x + x2 = 0 + 520
-2x + x2 = 0 + 520

Combine like terms: 0 + 520 = 520
-2x + x2 = 520

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 = 520 + 1

Reorder the terms:
1 + -2x + x2 = 520 + 1

Combine like terms: 520 + 1 = 521
1 + -2x + x2 = 521

Factor a perfect square on the left side:
(x + -1)(x + -1) = 521

Calculate the square root of the right side: 22.825424421

Break this problem into two subproblems by setting 
(x + -1) equal to 22.825424421 and -22.825424421.

Subproblem 1
x + -1 = 22.825424421

Simplifying
x + -1 = 22.825424421

Reorder the terms:
-1 + x = 22.825424421

Solving
-1 + x = 22.825424421

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 = 22.825424421 + 1

Combine like terms: -1 + 1 = 0
0 + x = 22.825424421 + 1
x = 22.825424421 + 1

Combine like terms: 22.825424421 + 1 = 23.825424421
x = 23.825424421

Simplifying
x = 23.825424421

Subproblem 2
x + -1 = -22.825424421

Simplifying
x + -1 = -22.825424421

Reorder the terms:
-1 + x = -22.825424421

Solving
-1 + x = -22.825424421

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 = -22.825424421 + 1

Combine like terms: -1 + 1 = 0
0 + x = -22.825424421 + 1
x = -22.825424421 + 1

Combine like terms: -22.825424421 + 1 = -21.825424421
x = -21.825424421

Simplifying
x = -21.825424421

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.825424421, -21.825424421}
Solution
x = {23.825424421, -21.825424421}