2x^2-360x=100

Solution for 2x^2-360x=100 equation:

Simplifying
2x2 + -360x = 100

Reorder the terms:
-360x + 2x2 = 100

Solving
-360x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + -360x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -360x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -180x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + -180x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + -180x + x2 = 0

Solving
-50 + -180x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -180x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -180x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -180x + x2 = 0 + 50
-180x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-180x + x2 = 50

The x term is -180x.  Take half its coefficient (-90).
Square it (8100) and add it to both sides.

Add '8100' to each side of the equation.
-180x + 8100 + x2 = 50 + 8100

Reorder the terms:
8100 + -180x + x2 = 50 + 8100

Combine like terms: 50 + 8100 = 8150
8100 + -180x + x2 = 8150

Factor a perfect square on the left side:
(x + -90)(x + -90) = 8150

Calculate the square root of the right side: 90.277350426

Break this problem into two subproblems by setting 
(x + -90) equal to 90.277350426 and -90.277350426.

Subproblem 1
x + -90 = 90.277350426

Simplifying
x + -90 = 90.277350426

Reorder the terms:
-90 + x = 90.277350426

Solving
-90 + x = 90.277350426

Solving for variable 'x'.

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

Add '90' to each side of the equation.
-90 + 90 + x = 90.277350426 + 90

Combine like terms: -90 + 90 = 0
0 + x = 90.277350426 + 90
x = 90.277350426 + 90

Combine like terms: 90.277350426 + 90 = 180.277350426
x = 180.277350426

Simplifying
x = 180.277350426

Subproblem 2
x + -90 = -90.277350426

Simplifying
x + -90 = -90.277350426

Reorder the terms:
-90 + x = -90.277350426

Solving
-90 + x = -90.277350426

Solving for variable 'x'.

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

Add '90' to each side of the equation.
-90 + 90 + x = -90.277350426 + 90

Combine like terms: -90 + 90 = 0
0 + x = -90.277350426 + 90
x = -90.277350426 + 90

Combine like terms: -90.277350426 + 90 = -0.277350426
x = -0.277350426

Simplifying
x = -0.277350426

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {180.277350426, -0.277350426}
Solution
x = {180.277350426, -0.277350426}