(x+0.1)(x)=-.00000002

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Solution for (x+0.1)(x)=-.00000002 equation: 


Simplifying
(x + 0.1)(x) = -0.00000002

Reorder the terms:
(0.1 + x)(x) = -0.00000002

Reorder the terms for easier multiplication:
x(0.1 + x) = -0.00000002
(0.1 * x + x * x) = -0.00000002
(0.1x + x2) = -0.00000002

Solving
0.1x + x2 = -0.00000002

Solving for variable 'x'.

Reorder the terms:
0.00000002 + 0.1x + x2 = -0.00000002 + 0.00000002

Combine like terms: -0.00000002 + 0.00000002 = 0.00000000
0.00000002 + 0.1x + x2 = 0.00000000

Begin completing the square.

Move the constant term to the right:

Add '-0.00000002' to each side of the equation.
0.00000002 + 0.1x + -0.00000002 + x2 = 0.00000000 + -0.00000002

Reorder the terms:
0.00000002 + -0.00000002 + 0.1x + x2 = 0.00000000 + -0.00000002

Combine like terms: 0.00000002 + -0.00000002 = 0.00000000
0.00000000 + 0.1x + x2 = 0.00000000 + -0.00000002
0.1x + x2 = 0.00000000 + -0.00000002

Combine like terms: 0.00000000 + -0.00000002 = -0.00000002
0.1x + x2 = -0.00000002

The x term is 0.1x.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1x + 0.0025 + x2 = -0.00000002 + 0.0025

Reorder the terms:
0.0025 + 0.1x + x2 = -0.00000002 + 0.0025

Combine like terms: -0.00000002 + 0.0025 = 0.00249998
0.0025 + 0.1x + x2 = 0.00249998

Factor a perfect square on the left side:
(x + 0.05)(x + 0.05) = 0.00249998

Calculate the square root of the right side: 0.0499998

Break this problem into two subproblems by setting 
(x + 0.05) equal to 0.0499998 and -0.0499998.


Subproblem 1
x + 0.05 = 0.0499998

Simplifying
x + 0.05 = 0.0499998

Reorder the terms:
0.05 + x = 0.0499998

Solving
0.05 + x = 0.0499998

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = 0.0499998 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = 0.0499998 + -0.05
x = 0.0499998 + -0.05

Combine like terms: 0.0499998 + -0.05 = -0.0000002
x = -0.0000002

Simplifying
x = -0.0000002


Subproblem 2
x + 0.05 = -0.0499998

Simplifying
x + 0.05 = -0.0499998

Reorder the terms:
0.05 + x = -0.0499998

Solving
0.05 + x = -0.0499998

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = -0.0499998 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = -0.0499998 + -0.05
x = -0.0499998 + -0.05

Combine like terms: -0.0499998 + -0.05 = -0.0999998
x = -0.0999998

Simplifying
x = -0.0999998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0000002, -0.0999998}

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