x^2-75x+800=0

Solution for x^2-75x+800=0 equation:

Simplifying
x2 + -75x + 800 = 0

Reorder the terms:
800 + -75x + x2 = 0

Solving
800 + -75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-800' to each side of the equation.
800 + -75x + -800 + x2 = 0 + -800

Reorder the terms:
800 + -800 + -75x + x2 = 0 + -800

Combine like terms: 800 + -800 = 0
0 + -75x + x2 = 0 + -800
-75x + x2 = 0 + -800

Combine like terms: 0 + -800 = -800
-75x + x2 = -800

The x term is -75x.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75x + 1406.25 + x2 = -800 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = -800 + 1406.25

Combine like terms: -800 + 1406.25 = 606.25
1406.25 + -75x + x2 = 606.25

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 606.25

Calculate the square root of the right side: 24.622144504

Break this problem into two subproblems by setting 
(x + -37.5) equal to 24.622144504 and -24.622144504.

Subproblem 1
x + -37.5 = 24.622144504

Simplifying
x + -37.5 = 24.622144504

Reorder the terms:
-37.5 + x = 24.622144504

Solving
-37.5 + x = 24.622144504

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = 24.622144504 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = 24.622144504 + 37.5
x = 24.622144504 + 37.5

Combine like terms: 24.622144504 + 37.5 = 62.122144504
x = 62.122144504

Simplifying
x = 62.122144504

Subproblem 2
x + -37.5 = -24.622144504

Simplifying
x + -37.5 = -24.622144504

Reorder the terms:
-37.5 + x = -24.622144504

Solving
-37.5 + x = -24.622144504

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = -24.622144504 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = -24.622144504 + 37.5
x = -24.622144504 + 37.5

Combine like terms: -24.622144504 + 37.5 = 12.877855496
x = 12.877855496

Simplifying
x = 12.877855496

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {62.122144504, 12.877855496}