0.012x^2-0.1x+0.16=0

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Solution for 0.012x^2-0.1x+0.16=0 equation: 


Simplifying
0.012x2 + -0.1x + 0.16 = 0

Reorder the terms:
0.16 + -0.1x + 0.012x2 = 0

Solving
0.16 + -0.1x + 0.012x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.012'.
13.33333333 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + -8.333333333x + -13.33333333 + x2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + -8.333333333x + x2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + -8.333333333x + x2 = 0 + -13.33333333
-8.333333333x + x2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
-8.333333333x + x2 = -13.33333333

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -13.33333333 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -13.33333333 + 17.36111111

Combine like terms: -13.33333333 + 17.36111111 = 4.02777778
17.36111111 + -8.333333333x + x2 = 4.02777778

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 4.02777778

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 2.00693243 and -2.00693243.


Subproblem 1
x + -4.166666667 = 2.00693243

Simplifying
x + -4.166666667 = 2.00693243

Reorder the terms:
-4.166666667 + x = 2.00693243

Solving
-4.166666667 + x = 2.00693243

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = 2.00693243 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 2.00693243 + 4.166666667
x = 2.00693243 + 4.166666667

Combine like terms: 2.00693243 + 4.166666667 = 6.173599097
x = 6.173599097

Simplifying
x = 6.173599097


Subproblem 2
x + -4.166666667 = -2.00693243

Simplifying
x + -4.166666667 = -2.00693243

Reorder the terms:
-4.166666667 + x = -2.00693243

Solving
-4.166666667 + x = -2.00693243

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = -2.00693243 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -2.00693243 + 4.166666667
x = -2.00693243 + 4.166666667

Combine like terms: -2.00693243 + 4.166666667 = 2.159734237
x = 2.159734237

Simplifying
x = 2.159734237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.173599097, 2.159734237}

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