4x^2-400x-401=0

Solution for 4x^2-400x-401=0 equation:

Simplifying
4x2 + -400x + -401 = 0

Reorder the terms:
-401 + -400x + 4x2 = 0

Solving
-401 + -400x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-100.25 + -100x + x2 = 0

Move the constant term to the right:

Add '100.25' to each side of the equation.
-100.25 + -100x + 100.25 + x2 = 0 + 100.25

Reorder the terms:
-100.25 + 100.25 + -100x + x2 = 0 + 100.25

Combine like terms: -100.25 + 100.25 = 0.00
0.00 + -100x + x2 = 0 + 100.25
-100x + x2 = 0 + 100.25

Combine like terms: 0 + 100.25 = 100.25
-100x + x2 = 100.25

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = 100.25 + 2500

Reorder the terms:
2500 + -100x + x2 = 100.25 + 2500

Combine like terms: 100.25 + 2500 = 2600.25
2500 + -100x + x2 = 2600.25

Factor a perfect square on the left side:
(x + -50)(x + -50) = 2600.25

Calculate the square root of the right side: 50.992646529

Break this problem into two subproblems by setting 
(x + -50) equal to 50.992646529 and -50.992646529.

Subproblem 1
x + -50 = 50.992646529

Simplifying
x + -50 = 50.992646529

Reorder the terms:
-50 + x = 50.992646529

Solving
-50 + x = 50.992646529

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = 50.992646529 + 50

Combine like terms: -50 + 50 = 0
0 + x = 50.992646529 + 50
x = 50.992646529 + 50

Combine like terms: 50.992646529 + 50 = 100.992646529
x = 100.992646529

Simplifying
x = 100.992646529

Subproblem 2
x + -50 = -50.992646529

Simplifying
x + -50 = -50.992646529

Reorder the terms:
-50 + x = -50.992646529

Solving
-50 + x = -50.992646529

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = -50.992646529 + 50

Combine like terms: -50 + 50 = 0
0 + x = -50.992646529 + 50
x = -50.992646529 + 50

Combine like terms: -50.992646529 + 50 = -0.992646529
x = -0.992646529

Simplifying
x = -0.992646529

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {100.992646529, -0.992646529}