x(x+1)=9999999

Solution for x(x+1)=9999999 equation:

Simplifying
x(x + 1) = 9999999

Reorder the terms:
x(1 + x) = 9999999
(1 * x + x * x) = 9999999
(1x + x2) = 9999999

Solving
1x + x2 = 9999999

Solving for variable 'x'.

Reorder the terms:
-9999999 + 1x + x2 = 9999999 + -9999999

Combine like terms: 9999999 + -9999999 = 0
-9999999 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9999999' to each side of the equation.
-9999999 + 1x + 9999999 + x2 = 0 + 9999999

Reorder the terms:
-9999999 + 9999999 + 1x + x2 = 0 + 9999999

Combine like terms: -9999999 + 9999999 = 0
0 + 1x + x2 = 0 + 9999999
1x + x2 = 0 + 9999999

Combine like terms: 0 + 9999999 = 9999999
1x + x2 = 9999999

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.
x + 0.25 + x2 = 9999999 + 0.25

Reorder the terms:
0.25 + x + x2 = 9999999 + 0.25

Combine like terms: 9999999 + 0.25 = 9999999.25
0.25 + x + x2 = 9999999.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 9999999.25

Calculate the square root of the right side: 3162.277541583

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3162.277541583 and -3162.277541583.

Subproblem 1
x + 0.5 = 3162.277541583

Simplifying
x + 0.5 = 3162.277541583

Reorder the terms:
0.5 + x = 3162.277541583

Solving
0.5 + x = 3162.277541583

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 = 3162.277541583 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3162.277541583 + -0.5
x = 3162.277541583 + -0.5

Combine like terms: 3162.277541583 + -0.5 = 3161.777541583
x = 3161.777541583

Simplifying
x = 3161.777541583

Subproblem 2
x + 0.5 = -3162.277541583

Simplifying
x + 0.5 = -3162.277541583

Reorder the terms:
0.5 + x = -3162.277541583

Solving
0.5 + x = -3162.277541583

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 = -3162.277541583 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3162.277541583 + -0.5
x = -3162.277541583 + -0.5

Combine like terms: -3162.277541583 + -0.5 = -3162.777541583
x = -3162.777541583

Simplifying
x = -3162.777541583

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3161.777541583, -3162.777541583}