0=x^2-x-400

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

Simplifying
0 = x2 + -1x + -400

Reorder the terms:
0 = -400 + -1x + x2

Solving
0 = -400 + -1x + x2

Solving for variable 'x'.

Combine like terms: 0 + 400 = 400
400 + x + -1x2 = -400 + -1x + x2 + 400 + x + -1x2

Reorder the terms:
400 + x + -1x2 = -400 + 400 + -1x + x + x2 + -1x2

Combine like terms: -400 + 400 = 0
400 + x + -1x2 = 0 + -1x + x + x2 + -1x2
400 + x + -1x2 = -1x + x + x2 + -1x2

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

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

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

Divide each side by '-1'.
-400 + -1x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -1x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -1x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -1x + x2 = 0 + 400
-1x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-1x + x2 = 400

The x term is x.  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 = 400 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 400 + 0.25

Combine like terms: 400 + 0.25 = 400.25
0.25 + -1x + x2 = 400.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 400.25

Calculate the square root of the right side: 20.006249024

Break this problem into two subproblems by setting 
(x + 0.5) equal to 20.006249024 and -20.006249024.

Subproblem 1
x + 0.5 = 20.006249024

Simplifying
x + 0.5 = 20.006249024

Reorder the terms:
0.5 + x = 20.006249024

Solving
0.5 + x = 20.006249024

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 = 20.006249024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 20.006249024 + -0.5
x = 20.006249024 + -0.5

Combine like terms: 20.006249024 + -0.5 = 19.506249024
x = 19.506249024

Simplifying
x = 19.506249024

Subproblem 2
x + 0.5 = -20.006249024

Simplifying
x + 0.5 = -20.006249024

Reorder the terms:
0.5 + x = -20.006249024

Solving
0.5 + x = -20.006249024

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 = -20.006249024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -20.006249024 + -0.5
x = -20.006249024 + -0.5

Combine like terms: -20.006249024 + -0.5 = -20.506249024
x = -20.506249024

Simplifying
x = -20.506249024

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.506249024, -20.506249024}