10000=x^2+x

Solution for 10000=x^2+x equation:

Simplifying
10000 = x2 + x

Reorder the terms:
10000 = x + x2

Solving
10000 = x + x2

Solving for variable 'x'.

Reorder the terms:
10000 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
10000 + -1x + -1x2 = 0 + x2 + -1x2
10000 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10000 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10000 + x + x2 = 0

Move the constant term to the right:

Add '10000' to each side of the equation.
-10000 + x + 10000 + x2 = 0 + 10000

Reorder the terms:
-10000 + 10000 + x + x2 = 0 + 10000

Combine like terms: -10000 + 10000 = 0
0 + x + x2 = 0 + 10000
x + x2 = 0 + 10000

Combine like terms: 0 + 10000 = 10000
x + x2 = 10000

The x term is x.  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.
 + 0.25 + x2 = 10000 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 10000 + 0.25

Combine like terms: 10000 + 0.25 = 10000.25
1.25 + x2 = 10000.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 10000.25

Calculate the square root of the right side: 100.001249992

Break this problem into two subproblems by setting 
(x + 0.5) equal to 100.001249992 and -100.001249992.

Subproblem 1
x + 0.5 = 100.001249992

Simplifying
x + 0.5 = 100.001249992

Reorder the terms:
0.5 + x = 100.001249992

Solving
0.5 + x = 100.001249992

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 = 100.001249992 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 100.001249992 + -0.5
x = 100.001249992 + -0.5

Combine like terms: 100.001249992 + -0.5 = 99.501249992
x = 99.501249992

Simplifying
x = 99.501249992

Subproblem 2
x + 0.5 = -100.001249992

Simplifying
x + 0.5 = -100.001249992

Reorder the terms:
0.5 + x = -100.001249992

Solving
0.5 + x = -100.001249992

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 = -100.001249992 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -100.001249992 + -0.5
x = -100.001249992 + -0.5

Combine like terms: -100.001249992 + -0.5 = -100.501249992
x = -100.501249992

Simplifying
x = -100.501249992

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {99.501249992, -100.501249992}