=50x^2-50x+1

Solution for =50x^2-50x+1 equation:

Simplifying
0 = 50x2 + -50x + 1

Reorder the terms:
0 = 1 + -50x + 50x2

Solving
0 = 1 + -50x + 50x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 50x + -50x2 = 1 + -50x + 50x2 + -1 + 50x + -50x2

Reorder the terms:
-1 + 50x + -50x2 = 1 + -1 + -50x + 50x + 50x2 + -50x2

Combine like terms: 1 + -1 = 0
-1 + 50x + -50x2 = 0 + -50x + 50x + 50x2 + -50x2
-1 + 50x + -50x2 = -50x + 50x + 50x2 + -50x2

Combine like terms: -50x + 50x = 0
-1 + 50x + -50x2 = 0 + 50x2 + -50x2
-1 + 50x + -50x2 = 50x2 + -50x2

Combine like terms: 50x2 + -50x2 = 0
-1 + 50x + -50x2 = 0

Begin completing the square.  Divide all terms by
-50 the coefficient of the squared term: 

Divide each side by '-50'.
0.02 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.02' to each side of the equation.
0.02 + -1x + -0.02 + x2 = 0 + -0.02

Reorder the terms:
0.02 + -0.02 + -1x + x2 = 0 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + -1x + x2 = 0 + -0.02
-1x + x2 = 0 + -0.02

Combine like terms: 0 + -0.02 = -0.02
-1x + x2 = -0.02

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.02 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.02 + 0.25

Combine like terms: -0.02 + 0.25 = 0.23
0.25 + -1x + x2 = 0.23

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.23

Calculate the square root of the right side: 0.479583152

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.479583152 and -0.479583152.

Subproblem 1
x + -0.5 = 0.479583152

Simplifying
x + -0.5 = 0.479583152

Reorder the terms:
-0.5 + x = 0.479583152

Solving
-0.5 + x = 0.479583152

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.479583152 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.479583152 + 0.5
x = 0.479583152 + 0.5

Combine like terms: 0.479583152 + 0.5 = 0.979583152
x = 0.979583152

Simplifying
x = 0.979583152

Subproblem 2
x + -0.5 = -0.479583152

Simplifying
x + -0.5 = -0.479583152

Reorder the terms:
-0.5 + x = -0.479583152

Solving
-0.5 + x = -0.479583152

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.479583152 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.479583152 + 0.5
x = -0.479583152 + 0.5

Combine like terms: -0.479583152 + 0.5 = 0.020416848
x = 0.020416848

Simplifying
x = 0.020416848

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.979583152, 0.020416848}