(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 = 0.00250002
0.0025 + 0.1x + x2 = 0.00250002

Factor a perfect square on the left side:
(x + 0.05)(x + 0.05) = 0.00250002

Calculate the square root of the right side: 0.0500002

Break this problem into two subproblems by setting 
(x + 0.05) equal to 0.0500002 and -0.0500002.

Subproblem 1

x + 0.05 = 0.0500002 Simplifying x + 0.05 = 0.0500002 Reorder the terms: 0.05 + x = 0.0500002 Solving 0.05 + x = 0.0500002 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 = 0.0500002 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.0500002 + -0.05 x = 0.0500002 + -0.05 Combine like terms: 0.0500002 + -0.05 = 0.0000002 x = 0.0000002 Simplifying x = 0.0000002

Subproblem 2

x + 0.05 = -0.0500002 Simplifying x + 0.05 = -0.0500002 Reorder the terms: 0.05 + x = -0.0500002 Solving 0.05 + x = -0.0500002 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 = -0.0500002 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.0500002 + -0.05 x = -0.0500002 + -0.05 Combine like terms: -0.0500002 + -0.05 = -0.1000002 x = -0.1000002 Simplifying x = -0.1000002

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.0000002, -0.1000002}

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