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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