x(x-1)=200000

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Solution for x(x-1)=200000 equation: 


Simplifying
x(x + -1) = 200000

Reorder the terms:
x(-1 + x) = 200000
(-1 * x + x * x) = 200000
(-1x + x2) = 200000

Solving
-1x + x2 = 200000

Solving for variable 'x'.

Reorder the terms:
-200000 + -1x + x2 = 200000 + -200000

Combine like terms: 200000 + -200000 = 0
-200000 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '200000' to each side of the equation.
-200000 + -1x + 200000 + x2 = 0 + 200000

Reorder the terms:
-200000 + 200000 + -1x + x2 = 0 + 200000

Combine like terms: -200000 + 200000 = 0
0 + -1x + x2 = 0 + 200000
-1x + x2 = 0 + 200000

Combine like terms: 0 + 200000 = 200000
-1x + x2 = 200000

The x term is -1x.  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 = 200000 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 200000 + 0.25

Combine like terms: 200000 + 0.25 = 200000.25
0.25 + -1x + x2 = 200000.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 200000.25

Calculate the square root of the right side: 447.213875008

Break this problem into two subproblems by setting 
(x + -0.5) equal to 447.213875008 and -447.213875008.


Subproblem 1
x + -0.5 = 447.213875008

Simplifying
x + -0.5 = 447.213875008

Reorder the terms:
-0.5 + x = 447.213875008

Solving
-0.5 + x = 447.213875008

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 = 447.213875008 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 447.213875008 + 0.5
x = 447.213875008 + 0.5

Combine like terms: 447.213875008 + 0.5 = 447.713875008
x = 447.713875008

Simplifying
x = 447.713875008


Subproblem 2
x + -0.5 = -447.213875008

Simplifying
x + -0.5 = -447.213875008

Reorder the terms:
-0.5 + x = -447.213875008

Solving
-0.5 + x = -447.213875008

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 = -447.213875008 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -447.213875008 + 0.5
x = -447.213875008 + 0.5

Combine like terms: -447.213875008 + 0.5 = -446.713875008
x = -446.713875008

Simplifying
x = -446.713875008


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {447.713875008, -446.713875008}

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