x^2-400x-1000=0

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Solution for x^2-400x-1000=0 equation: 


Simplifying
x2 + -400x + -1000 = 0

Reorder the terms:
-1000 + -400x + x2 = 0

Solving
-1000 + -400x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + -400x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + -400x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + -400x + x2 = 0 + 1000
-400x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
-400x + x2 = 1000

The x term is -400x.  Take half its coefficient (-200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
-400x + 40000 + x2 = 1000 + 40000

Reorder the terms:
40000 + -400x + x2 = 1000 + 40000

Combine like terms: 1000 + 40000 = 41000
40000 + -400x + x2 = 41000

Factor a perfect square on the left side:
(x + -200)(x + -200) = 41000

Calculate the square root of the right side: 202.484567313

Break this problem into two subproblems by setting 
(x + -200) equal to 202.484567313 and -202.484567313.


Subproblem 1
x + -200 = 202.484567313

Simplifying
x + -200 = 202.484567313

Reorder the terms:
-200 + x = 202.484567313

Solving
-200 + x = 202.484567313

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = 202.484567313 + 200

Combine like terms: -200 + 200 = 0
0 + x = 202.484567313 + 200
x = 202.484567313 + 200

Combine like terms: 202.484567313 + 200 = 402.484567313
x = 402.484567313

Simplifying
x = 402.484567313


Subproblem 2
x + -200 = -202.484567313

Simplifying
x + -200 = -202.484567313

Reorder the terms:
-200 + x = -202.484567313

Solving
-200 + x = -202.484567313

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = -202.484567313 + 200

Combine like terms: -200 + 200 = 0
0 + x = -202.484567313 + 200
x = -202.484567313 + 200

Combine like terms: -202.484567313 + 200 = -2.484567313
x = -2.484567313

Simplifying
x = -2.484567313


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {402.484567313, -2.484567313}

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