x^2+1000x-1000=0

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


Simplifying
x2 + 1000x + -1000 = 0

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

Solving
-1000 + 1000x + 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 + 1000x + 1000 + x2 = 0 + 1000

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

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

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

The x term is 1000x.  Take half its coefficient (500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
1000x + 250000 + x2 = 1000 + 250000

Reorder the terms:
250000 + 1000x + x2 = 1000 + 250000

Combine like terms: 1000 + 250000 = 251000
250000 + 1000x + x2 = 251000

Factor a perfect square on the left side:
(x + 500)(x + 500) = 251000

Calculate the square root of the right side: 500.999001995

Break this problem into two subproblems by setting 
(x + 500) equal to 500.999001995 and -500.999001995.


Subproblem 1
x + 500 = 500.999001995

Simplifying
x + 500 = 500.999001995

Reorder the terms:
500 + x = 500.999001995

Solving
500 + x = 500.999001995

Solving for variable 'x'.

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

Add '-500' to each side of the equation.
500 + -500 + x = 500.999001995 + -500

Combine like terms: 500 + -500 = 0
0 + x = 500.999001995 + -500
x = 500.999001995 + -500

Combine like terms: 500.999001995 + -500 = 0.999001995
x = 0.999001995

Simplifying
x = 0.999001995


Subproblem 2
x + 500 = -500.999001995

Simplifying
x + 500 = -500.999001995

Reorder the terms:
500 + x = -500.999001995

Solving
500 + x = -500.999001995

Solving for variable 'x'.

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

Add '-500' to each side of the equation.
500 + -500 + x = -500.999001995 + -500

Combine like terms: 500 + -500 = 0
0 + x = -500.999001995 + -500
x = -500.999001995 + -500

Combine like terms: -500.999001995 + -500 = -1000.999001995
x = -1000.999001995

Simplifying
x = -1000.999001995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.999001995, -1000.999001995}

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