x(2x-100)=800

Solution for x(2x-100)=800 equation:

Simplifying
x(2x + -100) = 800

Reorder the terms:
x(-100 + 2x) = 800
(-100 * x + 2x * x) = 800
(-100x + 2x2) = 800

Solving
-100x + 2x2 = 800

Solving for variable 'x'.

Reorder the terms:
-800 + -100x + 2x2 = 800 + -800

Combine like terms: 800 + -800 = 0
-800 + -100x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-400 + -50x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-400 + -50x + x2)' equal to zero and attempt to solve:

Simplifying
-400 + -50x + x2 = 0

Solving
-400 + -50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -50x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -50x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -50x + x2 = 0 + 400
-50x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-50x + x2 = 400

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = 400 + 625

Reorder the terms:
625 + -50x + x2 = 400 + 625

Combine like terms: 400 + 625 = 1025
625 + -50x + x2 = 1025

Factor a perfect square on the left side:
(x + -25)(x + -25) = 1025

Calculate the square root of the right side: 32.015621187

Break this problem into two subproblems by setting 
(x + -25) equal to 32.015621187 and -32.015621187.

Subproblem 1
x + -25 = 32.015621187

Simplifying
x + -25 = 32.015621187

Reorder the terms:
-25 + x = 32.015621187

Solving
-25 + x = 32.015621187

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = 32.015621187 + 25

Combine like terms: -25 + 25 = 0
0 + x = 32.015621187 + 25
x = 32.015621187 + 25

Combine like terms: 32.015621187 + 25 = 57.015621187
x = 57.015621187

Simplifying
x = 57.015621187

Subproblem 2
x + -25 = -32.015621187

Simplifying
x + -25 = -32.015621187

Reorder the terms:
-25 + x = -32.015621187

Solving
-25 + x = -32.015621187

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = -32.015621187 + 25

Combine like terms: -25 + 25 = 0
0 + x = -32.015621187 + 25
x = -32.015621187 + 25

Combine like terms: -32.015621187 + 25 = -7.015621187
x = -7.015621187

Simplifying
x = -7.015621187

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {57.015621187, -7.015621187}
Solution
x = {57.015621187, -7.015621187}