x(0.01+x)=0.01(0.01-x)

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Solution for x(0.01+x)=0.01(0.01-x) equation: 


Simplifying
x(0.01 + x) = 0.01(0.01 + -1x)
(0.01 * x + x * x) = 0.01(0.01 + -1x)
(0.01x + x2) = 0.01(0.01 + -1x)
0.01x + x2 = (0.01 * 0.01 + -1x * 0.01)
0.01x + x2 = (0.0001 + -0.01x)

Solving
0.01x + x2 = 0.0001 + -0.01x

Solving for variable 'x'.

Reorder the terms:
-0.0001 + 0.01x + 0.01x + x2 = 0.0001 + -0.01x + -0.0001 + 0.01x

Combine like terms: 0.01x + 0.01x = 0.02x
-0.0001 + 0.02x + x2 = 0.0001 + -0.01x + -0.0001 + 0.01x

Reorder the terms:
-0.0001 + 0.02x + x2 = 0.0001 + -0.0001 + -0.01x + 0.01x

Combine like terms: 0.0001 + -0.0001 = 0.0000
-0.0001 + 0.02x + x2 = 0.0000 + -0.01x + 0.01x
-0.0001 + 0.02x + x2 = -0.01x + 0.01x

Combine like terms: -0.01x + 0.01x = 0.00
-0.0001 + 0.02x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.0001' to each side of the equation.
-0.0001 + 0.02x + 0.0001 + x2 = 0.00 + 0.0001

Reorder the terms:
-0.0001 + 0.0001 + 0.02x + x2 = 0.00 + 0.0001

Combine like terms: -0.0001 + 0.0001 = 0.0000
0.0000 + 0.02x + x2 = 0.00 + 0.0001
0.02x + x2 = 0.00 + 0.0001

Combine like terms: 0.00 + 0.0001 = 0.0001
0.02x + x2 = 0.0001

The x term is 0.02x.  Take half its coefficient (0.01).
Square it (0.0001) and add it to both sides.

Add '0.0001' to each side of the equation.
0.02x + 0.0001 + x2 = 0.0001 + 0.0001

Reorder the terms:
0.0001 + 0.02x + x2 = 0.0001 + 0.0001

Combine like terms: 0.0001 + 0.0001 = 0.0002
0.0001 + 0.02x + x2 = 0.0002

Factor a perfect square on the left side:
(x + 0.01)(x + 0.01) = 0.0002

Calculate the square root of the right side: 0.014142136

Break this problem into two subproblems by setting 
(x + 0.01) equal to 0.014142136 and -0.014142136.


Subproblem 1
x + 0.01 = 0.014142136

Simplifying
x + 0.01 = 0.014142136

Reorder the terms:
0.01 + x = 0.014142136

Solving
0.01 + x = 0.014142136

Solving for variable 'x'.

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

Add '-0.01' to each side of the equation.
0.01 + -0.01 + x = 0.014142136 + -0.01

Combine like terms: 0.01 + -0.01 = 0.00
0.00 + x = 0.014142136 + -0.01
x = 0.014142136 + -0.01

Combine like terms: 0.014142136 + -0.01 = 0.004142136
x = 0.004142136

Simplifying
x = 0.004142136


Subproblem 2
x + 0.01 = -0.014142136

Simplifying
x + 0.01 = -0.014142136

Reorder the terms:
0.01 + x = -0.014142136

Solving
0.01 + x = -0.014142136

Solving for variable 'x'.

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

Add '-0.01' to each side of the equation.
0.01 + -0.01 + x = -0.014142136 + -0.01

Combine like terms: 0.01 + -0.01 = 0.00
0.00 + x = -0.014142136 + -0.01
x = -0.014142136 + -0.01

Combine like terms: -0.014142136 + -0.01 = -0.024142136
x = -0.024142136

Simplifying
x = -0.024142136


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.004142136, -0.024142136}

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