800=2x^2-58x-352

Solution for 800=2x^2-58x-352 equation:

Simplifying
800 = 2x2 + -58x + -352

Reorder the terms:
800 = -352 + -58x + 2x2

Solving
800 = -352 + -58x + 2x2

Solving for variable 'x'.

Combine like terms: 800 + 352 = 1152
1152 + 58x + -2x2 = -352 + -58x + 2x2 + 352 + 58x + -2x2

Reorder the terms:
1152 + 58x + -2x2 = -352 + 352 + -58x + 58x + 2x2 + -2x2

Combine like terms: -352 + 352 = 0
1152 + 58x + -2x2 = 0 + -58x + 58x + 2x2 + -2x2
1152 + 58x + -2x2 = -58x + 58x + 2x2 + -2x2

Combine like terms: -58x + 58x = 0
1152 + 58x + -2x2 = 0 + 2x2 + -2x2
1152 + 58x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1152 + 58x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(576 + 29x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(576 + 29x + -1x2)' equal to zero and attempt to solve:

Simplifying
576 + 29x + -1x2 = 0

Solving
576 + 29x + -1x2 = 0

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

Divide each side by '-1'.
-576 + -29x + x2 = 0

Move the constant term to the right:

Add '576' to each side of the equation.
-576 + -29x + 576 + x2 = 0 + 576

Reorder the terms:
-576 + 576 + -29x + x2 = 0 + 576

Combine like terms: -576 + 576 = 0
0 + -29x + x2 = 0 + 576
-29x + x2 = 0 + 576

Combine like terms: 0 + 576 = 576
-29x + x2 = 576

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = 576 + 210.25

Reorder the terms:
210.25 + -29x + x2 = 576 + 210.25

Combine like terms: 576 + 210.25 = 786.25
210.25 + -29x + x2 = 786.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 786.25

Calculate the square root of the right side: 28.040149786

Break this problem into two subproblems by setting 
(x + -14.5) equal to 28.040149786 and -28.040149786.

Subproblem 1
x + -14.5 = 28.040149786

Simplifying
x + -14.5 = 28.040149786

Reorder the terms:
-14.5 + x = 28.040149786

Solving
-14.5 + x = 28.040149786

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = 28.040149786 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 28.040149786 + 14.5
x = 28.040149786 + 14.5

Combine like terms: 28.040149786 + 14.5 = 42.540149786
x = 42.540149786

Simplifying
x = 42.540149786

Subproblem 2
x + -14.5 = -28.040149786

Simplifying
x + -14.5 = -28.040149786

Reorder the terms:
-14.5 + x = -28.040149786

Solving
-14.5 + x = -28.040149786

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = -28.040149786 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -28.040149786 + 14.5
x = -28.040149786 + 14.5

Combine like terms: -28.040149786 + 14.5 = -13.540149786
x = -13.540149786

Simplifying
x = -13.540149786

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.540149786, -13.540149786}
Solution
x = {42.540149786, -13.540149786}