(25x^2-100x+50)+(50x-50)(2x)-(20x)(5-5x)-50x^2=0

Solution for (25x^2-100x+50)+(50x-50)(2x)-(20x)(5-5x)-50x^2=0 equation:

Simplifying
(25x2 + -100x + 50) + (50x + -50)(2x) + -1(20x)(5 + -5x) + -50x2 = 0

Reorder the terms:
(50 + -100x + 25x2) + (50x + -50)(2x) + -1(20x)(5 + -5x) + -50x2 = 0

Remove parenthesis around (50 + -100x + 25x2)
50 + -100x + 25x2 + (50x + -50)(2x) + -1(20x)(5 + -5x) + -50x2 = 0

Reorder the terms:
50 + -100x + 25x2 + (-50 + 50x)(2x) + -1(20x)(5 + -5x) + -50x2 = 0

Remove parenthesis around (2x)
50 + -100x + 25x2 + (-50 + 50x) * 2x + -1(20x)(5 + -5x) + -50x2 = 0

Reorder the terms for easier multiplication:
50 + -100x + 25x2 + 2x(-50 + 50x) + -1(20x)(5 + -5x) + -50x2 = 0
50 + -100x + 25x2 + (-50 * 2x + 50x * 2x) + -1(20x)(5 + -5x) + -50x2 = 0
50 + -100x + 25x2 + (-100x + 100x2) + -1(20x)(5 + -5x) + -50x2 = 0

Remove parenthesis around (20x)
50 + -100x + 25x2 + -100x + 100x2 + -1 * 20x(5 + -5x) + -50x2 = 0

Multiply -1 * 20
50 + -100x + 25x2 + -100x + 100x2 + -20x(5 + -5x) + -50x2 = 0
50 + -100x + 25x2 + -100x + 100x2 + (5 * -20x + -5x * -20x) + -50x2 = 0
50 + -100x + 25x2 + -100x + 100x2 + (-100x + 100x2) + -50x2 = 0

Reorder the terms:
50 + -100x + -100x + -100x + 25x2 + 100x2 + 100x2 + -50x2 = 0

Combine like terms: -100x + -100x = -200x
50 + -200x + -100x + 25x2 + 100x2 + 100x2 + -50x2 = 0

Combine like terms: -200x + -100x = -300x
50 + -300x + 25x2 + 100x2 + 100x2 + -50x2 = 0

Combine like terms: 25x2 + 100x2 = 125x2
50 + -300x + 125x2 + 100x2 + -50x2 = 0

Combine like terms: 125x2 + 100x2 = 225x2
50 + -300x + 225x2 + -50x2 = 0

Combine like terms: 225x2 + -50x2 = 175x2
50 + -300x + 175x2 = 0

Solving
50 + -300x + 175x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(2 + -12x + 7x2) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(2 + -12x + 7x2)' equal to zero and attempt to solve:

Simplifying
2 + -12x + 7x2 = 0

Solving
2 + -12x + 7x2 = 0

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

Divide each side by '7'.
0.2857142857 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -1.714285714x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -1.714285714x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -1.714285714x + x2 = 0 + -0.2857142857
-1.714285714x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-1.714285714x + x2 = -0.2857142857

The x term is -1.714285714x.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714x + 0.7346938773 + x2 = -0.2857142857 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = -0.2857142857 + 0.7346938773

Combine like terms: -0.2857142857 + 0.7346938773 = 0.4489795916
0.7346938773 + -1.714285714x + x2 = 0.4489795916

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 0.4489795916

Calculate the square root of the right side: 0.670059394

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 0.670059394 and -0.670059394.

Subproblem 1
x + -0.857142857 = 0.670059394

Simplifying
x + -0.857142857 = 0.670059394

Reorder the terms:
-0.857142857 + x = 0.670059394

Solving
-0.857142857 + x = 0.670059394

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = 0.670059394 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = 0.670059394 + 0.857142857
x = 0.670059394 + 0.857142857

Combine like terms: 0.670059394 + 0.857142857 = 1.527202251
x = 1.527202251

Simplifying
x = 1.527202251

Subproblem 2
x + -0.857142857 = -0.670059394

Simplifying
x + -0.857142857 = -0.670059394

Reorder the terms:
-0.857142857 + x = -0.670059394

Solving
-0.857142857 + x = -0.670059394

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = -0.670059394 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = -0.670059394 + 0.857142857
x = -0.670059394 + 0.857142857

Combine like terms: -0.670059394 + 0.857142857 = 0.187083463
x = 0.187083463

Simplifying
x = 0.187083463

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.527202251, 0.187083463}
Solution
x = {1.527202251, 0.187083463}