10x^2-401x-4000=0

Solution for 10x^2-401x-4000=0 equation:

Simplifying
10x2 + -401x + -4000 = 0

Reorder the terms:
-4000 + -401x + 10x2 = 0

Solving
-4000 + -401x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-400 + -40.1x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -40.1x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -40.1x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -40.1x + x2 = 0 + 400
-40.1x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-40.1x + x2 = 400

The x term is -40.1x.  Take half its coefficient (-20.05).
Square it (402.0025) and add it to both sides.

Add '402.0025' to each side of the equation.
-40.1x + 402.0025 + x2 = 400 + 402.0025

Reorder the terms:
402.0025 + -40.1x + x2 = 400 + 402.0025

Combine like terms: 400 + 402.0025 = 802.0025
402.0025 + -40.1x + x2 = 802.0025

Factor a perfect square on the left side:
(x + -20.05)(x + -20.05) = 802.0025

Calculate the square root of the right side: 28.319648656

Break this problem into two subproblems by setting 
(x + -20.05) equal to 28.319648656 and -28.319648656.

Subproblem 1
x + -20.05 = 28.319648656

Simplifying
x + -20.05 = 28.319648656

Reorder the terms:
-20.05 + x = 28.319648656

Solving
-20.05 + x = 28.319648656

Solving for variable 'x'.

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

Add '20.05' to each side of the equation.
-20.05 + 20.05 + x = 28.319648656 + 20.05

Combine like terms: -20.05 + 20.05 = 0.00
0.00 + x = 28.319648656 + 20.05
x = 28.319648656 + 20.05

Combine like terms: 28.319648656 + 20.05 = 48.369648656
x = 48.369648656

Simplifying
x = 48.369648656

Subproblem 2
x + -20.05 = -28.319648656

Simplifying
x + -20.05 = -28.319648656

Reorder the terms:
-20.05 + x = -28.319648656

Solving
-20.05 + x = -28.319648656

Solving for variable 'x'.

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

Add '20.05' to each side of the equation.
-20.05 + 20.05 + x = -28.319648656 + 20.05

Combine like terms: -20.05 + 20.05 = 0.00
0.00 + x = -28.319648656 + 20.05
x = -28.319648656 + 20.05

Combine like terms: -28.319648656 + 20.05 = -8.269648656
x = -8.269648656

Simplifying
x = -8.269648656

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.369648656, -8.269648656}