-2x^2+70x+520=0

Solution for -2x^2+70x+520=0 equation:

Simplifying
-2x2 + 70x + 520 = 0

Reorder the terms:
520 + 70x + -2x2 = 0

Solving
520 + 70x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(260 + 35x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(260 + 35x + -1x2)' equal to zero and attempt to solve:

Simplifying
260 + 35x + -1x2 = 0

Solving
260 + 35x + -1x2 = 0

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

Divide each side by '-1'.
-260 + -35x + x2 = 0

Move the constant term to the right:

Add '260' to each side of the equation.
-260 + -35x + 260 + x2 = 0 + 260

Reorder the terms:
-260 + 260 + -35x + x2 = 0 + 260

Combine like terms: -260 + 260 = 0
0 + -35x + x2 = 0 + 260
-35x + x2 = 0 + 260

Combine like terms: 0 + 260 = 260
-35x + x2 = 260

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = 260 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 260 + 306.25

Combine like terms: 260 + 306.25 = 566.25
306.25 + -35x + x2 = 566.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 566.25

Calculate the square root of the right side: 23.796008069

Break this problem into two subproblems by setting 
(x + -17.5) equal to 23.796008069 and -23.796008069.

Subproblem 1
x + -17.5 = 23.796008069

Simplifying
x + -17.5 = 23.796008069

Reorder the terms:
-17.5 + x = 23.796008069

Solving
-17.5 + x = 23.796008069

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 23.796008069 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 23.796008069 + 17.5
x = 23.796008069 + 17.5

Combine like terms: 23.796008069 + 17.5 = 41.296008069
x = 41.296008069

Simplifying
x = 41.296008069

Subproblem 2
x + -17.5 = -23.796008069

Simplifying
x + -17.5 = -23.796008069

Reorder the terms:
-17.5 + x = -23.796008069

Solving
-17.5 + x = -23.796008069

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -23.796008069 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -23.796008069 + 17.5
x = -23.796008069 + 17.5

Combine like terms: -23.796008069 + 17.5 = -6.296008069
x = -6.296008069

Simplifying
x = -6.296008069

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.296008069, -6.296008069}
Solution
x = {41.296008069, -6.296008069}