x^2+1000000x-1000000=0

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Solution for x^2+1000000x-1000000=0 equation: 


Simplifying
x2 + 1000000x + -1000000 = 0

Reorder the terms:
-1000000 + 1000000x + x2 = 0

Solving
-1000000 + 1000000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1000000' to each side of the equation.
-1000000 + 1000000x + 1000000 + x2 = 0 + 1000000

Reorder the terms:
-1000000 + 1000000 + 1000000x + x2 = 0 + 1000000

Combine like terms: -1000000 + 1000000 = 0
0 + 1000000x + x2 = 0 + 1000000
1000000x + x2 = 0 + 1000000

Combine like terms: 0 + 1000000 = 1000000
1000000x + x2 = 1000000

The x term is 1000000x.  Take half its coefficient (500000).
Square it (250000000000) and add it to both sides.

Add '250000000000' to each side of the equation.
1000000x + 250000000000 + x2 = 1000000 + 250000000000

Reorder the terms:
250000000000 + 1000000x + x2 = 1000000 + 250000000000

Combine like terms: 1000000 + 250000000000 = 250001000000
250000000000 + 1000000x + x2 = 250001000000

Factor a perfect square on the left side:
(x + 500000)(x + 500000) = 250001000000

Calculate the square root of the right side: 500000.999999

Break this problem into two subproblems by setting 
(x + 500000) equal to 500000.999999 and -500000.999999.


Subproblem 1
x + 500000 = 500000.999999

Simplifying
x + 500000 = 500000.999999

Reorder the terms:
500000 + x = 500000.999999

Solving
500000 + x = 500000.999999

Solving for variable 'x'.

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

Add '-500000' to each side of the equation.
500000 + -500000 + x = 500000.999999 + -500000

Combine like terms: 500000 + -500000 = 0
0 + x = 500000.999999 + -500000
x = 500000.999999 + -500000

Combine like terms: 500000.999999 + -500000 = 0.999999
x = 0.999999

Simplifying
x = 0.999999


Subproblem 2
x + 500000 = -500000.999999

Simplifying
x + 500000 = -500000.999999

Reorder the terms:
500000 + x = -500000.999999

Solving
500000 + x = -500000.999999

Solving for variable 'x'.

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

Add '-500000' to each side of the equation.
500000 + -500000 + x = -500000.999999 + -500000

Combine like terms: 500000 + -500000 = 0
0 + x = -500000.999999 + -500000
x = -500000.999999 + -500000

Combine like terms: -500000.999999 + -500000 = -1000000.999999
x = -1000000.999999

Simplifying
x = -1000000.999999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.999999, -1000000.999999}

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