-0.000018x^2+0.012x-0.1=0

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Solution for -0.000018x^2+0.012x-0.1=0 equation: 


Simplifying
-0.000018x2 + 0.012x + -0.1 = 0

Reorder the terms:
-0.1 + 0.012x + -0.000018x2 = 0

Solving
-0.1 + 0.012x + -0.000018x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.000018 the coefficient of the squared term: 

Divide each side by '-0.000018'.
5555.555556 + -666.6666667x + x2 = 0

Move the constant term to the right:

Add '-5555.555556' to each side of the equation.
5555.555556 + -666.6666667x + -5555.555556 + x2 = 0 + -5555.555556

Reorder the terms:
5555.555556 + -5555.555556 + -666.6666667x + x2 = 0 + -5555.555556

Combine like terms: 5555.555556 + -5555.555556 = 0.000000
0.000000 + -666.6666667x + x2 = 0 + -5555.555556
-666.6666667x + x2 = 0 + -5555.555556

Combine like terms: 0 + -5555.555556 = -5555.555556
-666.6666667x + x2 = -5555.555556

The x term is -666.6666667x.  Take half its coefficient (-333.3333334).
Square it (111111.1112) and add it to both sides.

Add '111111.1112' to each side of the equation.
-666.6666667x + 111111.1112 + x2 = -5555.555556 + 111111.1112

Reorder the terms:
111111.1112 + -666.6666667x + x2 = -5555.555556 + 111111.1112

Combine like terms: -5555.555556 + 111111.1112 = 105555.555644
111111.1112 + -666.6666667x + x2 = 105555.555644

Factor a perfect square on the left side:
(x + -333.3333334)(x + -333.3333334) = 105555.555644

Calculate the square root of the right side: 324.893144963

Break this problem into two subproblems by setting 
(x + -333.3333334) equal to 324.893144963 and -324.893144963.


Subproblem 1
x + -333.3333334 = 324.893144963

Simplifying
x + -333.3333334 = 324.893144963

Reorder the terms:
-333.3333334 + x = 324.893144963

Solving
-333.3333334 + x = 324.893144963

Solving for variable 'x'.

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

Add '333.3333334' to each side of the equation.
-333.3333334 + 333.3333334 + x = 324.893144963 + 333.3333334

Combine like terms: -333.3333334 + 333.3333334 = 0.0000000
0.0000000 + x = 324.893144963 + 333.3333334
x = 324.893144963 + 333.3333334

Combine like terms: 324.893144963 + 333.3333334 = 658.226478363
x = 658.226478363

Simplifying
x = 658.226478363


Subproblem 2
x + -333.3333334 = -324.893144963

Simplifying
x + -333.3333334 = -324.893144963

Reorder the terms:
-333.3333334 + x = -324.893144963

Solving
-333.3333334 + x = -324.893144963

Solving for variable 'x'.

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

Add '333.3333334' to each side of the equation.
-333.3333334 + 333.3333334 + x = -324.893144963 + 333.3333334

Combine like terms: -333.3333334 + 333.3333334 = 0.0000000
0.0000000 + x = -324.893144963 + 333.3333334
x = -324.893144963 + 333.3333334

Combine like terms: -324.893144963 + 333.3333334 = 8.440188437
x = 8.440188437

Simplifying
x = 8.440188437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {658.226478363, 8.440188437}

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