-2x^2+450x+-100=0

Solution for -2x^2+450x+-100=0 equation:

Simplifying
-2x2 + 450x + -100 = 0

Reorder the terms:
-100 + 450x + -2x2 = 0

Solving
-100 + 450x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 225x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + 225x + -1x2)' equal to zero and attempt to solve:

Simplifying
-50 + 225x + -1x2 = 0

Solving
-50 + 225x + -1x2 = 0

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

Divide each side by '-1'.
50 + -225x + x2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -225x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + -225x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -225x + x2 = 0 + -50
-225x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
-225x + x2 = -50

The x term is -225x.  Take half its coefficient (-112.5).
Square it (12656.25) and add it to both sides.

Add '12656.25' to each side of the equation.
-225x + 12656.25 + x2 = -50 + 12656.25

Reorder the terms:
12656.25 + -225x + x2 = -50 + 12656.25

Combine like terms: -50 + 12656.25 = 12606.25
12656.25 + -225x + x2 = 12606.25

Factor a perfect square on the left side:
(x + -112.5)(x + -112.5) = 12606.25

Calculate the square root of the right side: 112.277557864

Break this problem into two subproblems by setting 
(x + -112.5) equal to 112.277557864 and -112.277557864.

Subproblem 1
x + -112.5 = 112.277557864

Simplifying
x + -112.5 = 112.277557864

Reorder the terms:
-112.5 + x = 112.277557864

Solving
-112.5 + x = 112.277557864

Solving for variable 'x'.

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

Add '112.5' to each side of the equation.
-112.5 + 112.5 + x = 112.277557864 + 112.5

Combine like terms: -112.5 + 112.5 = 0.0
0.0 + x = 112.277557864 + 112.5
x = 112.277557864 + 112.5

Combine like terms: 112.277557864 + 112.5 = 224.777557864
x = 224.777557864

Simplifying
x = 224.777557864

Subproblem 2
x + -112.5 = -112.277557864

Simplifying
x + -112.5 = -112.277557864

Reorder the terms:
-112.5 + x = -112.277557864

Solving
-112.5 + x = -112.277557864

Solving for variable 'x'.

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

Add '112.5' to each side of the equation.
-112.5 + 112.5 + x = -112.277557864 + 112.5

Combine like terms: -112.5 + 112.5 = 0.0
0.0 + x = -112.277557864 + 112.5
x = -112.277557864 + 112.5

Combine like terms: -112.277557864 + 112.5 = 0.222442136
x = 0.222442136

Simplifying
x = 0.222442136

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {224.777557864, 0.222442136}
Solution
x = {224.777557864, 0.222442136}