x(0.1x-1)=0.00000014

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Solution for x(0.1x-1)=0.00000014 equation: 


Simplifying
x(0.1x + -1) = 0.00000014

Reorder the terms:
x(-1 + 0.1x) = 0.00000014
(-1 * x + 0.1x * x) = 0.00000014
(-1x + 0.1x2) = 0.00000014

Solving
-1x + 0.1x2 = 0.00000014

Solving for variable 'x'.

Reorder the terms:
-0.00000014 + -1x + 0.1x2 = 0.00000014 + -0.00000014

Combine like terms: 0.00000014 + -0.00000014 = 0.00000000
-0.00000014 + -1x + 0.1x2 = 0.00000000

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

Divide each side by '0.1'.
-0.0000014 + -10x + x2 = 0.0000000

Move the constant term to the right:

Add '0.0000014' to each side of the equation.
-0.0000014 + -10x + 0.0000014 + x2 = 0.0000000 + 0.0000014

Reorder the terms:
-0.0000014 + 0.0000014 + -10x + x2 = 0.0000000 + 0.0000014

Combine like terms: -0.0000014 + 0.0000014 = 0.0000000
0.0000000 + -10x + x2 = 0.0000000 + 0.0000014
-10x + x2 = 0.0000000 + 0.0000014

Combine like terms: 0.0000000 + 0.0000014 = 0.0000014
-10x + x2 = 0.0000014

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 0.0000014 + 25

Reorder the terms:
25 + -10x + x2 = 0.0000014 + 25

Combine like terms: 0.0000014 + 25 = 25.0000014
25 + -10x + x2 = 25.0000014

Factor a perfect square on the left side:
(x + -5)(x + -5) = 25.0000014

Calculate the square root of the right side: 5.00000014

Break this problem into two subproblems by setting 
(x + -5) equal to 5.00000014 and -5.00000014.


Subproblem 1
x + -5 = 5.00000014

Simplifying
x + -5 = 5.00000014

Reorder the terms:
-5 + x = 5.00000014

Solving
-5 + x = 5.00000014

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.00000014 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.00000014 + 5
x = 5.00000014 + 5

Combine like terms: 5.00000014 + 5 = 10.00000014
x = 10.00000014

Simplifying
x = 10.00000014


Subproblem 2
x + -5 = -5.00000014

Simplifying
x + -5 = -5.00000014

Reorder the terms:
-5 + x = -5.00000014

Solving
-5 + x = -5.00000014

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.00000014 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.00000014 + 5
x = -5.00000014 + 5

Combine like terms: -5.00000014 + 5 = -0.00000014
x = -0.00000014

Simplifying
x = -0.00000014


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.00000014, -0.00000014}

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