3x^2-1.862x+0.106=0

Solution for 3x^2-1.862x+0.106=0 equation:

Simplifying
3x2 + -1.862x + 0.106 = 0

Reorder the terms:
0.106 + -1.862x + 3x2 = 0

Solving
0.106 + -1.862x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
0.03533333333 + -0.6206666667x + x2 = 0

Move the constant term to the right:

Add '-0.03533333333' to each side of the equation.
0.03533333333 + -0.6206666667x + -0.03533333333 + x2 = 0 + -0.03533333333

Reorder the terms:
0.03533333333 + -0.03533333333 + -0.6206666667x + x2 = 0 + -0.03533333333

Combine like terms: 0.03533333333 + -0.03533333333 = 0.00000000000
0.00000000000 + -0.6206666667x + x2 = 0 + -0.03533333333
-0.6206666667x + x2 = 0 + -0.03533333333

Combine like terms: 0 + -0.03533333333 = -0.03533333333
-0.6206666667x + x2 = -0.03533333333

The x term is -0.6206666667x.  Take half its coefficient (-0.3103333334).
Square it (0.09630677782) and add it to both sides.

Add '0.09630677782' to each side of the equation.
-0.6206666667x + 0.09630677782 + x2 = -0.03533333333 + 0.09630677782

Reorder the terms:
0.09630677782 + -0.6206666667x + x2 = -0.03533333333 + 0.09630677782

Combine like terms: -0.03533333333 + 0.09630677782 = 0.06097344449
0.09630677782 + -0.6206666667x + x2 = 0.06097344449

Factor a perfect square on the left side:
(x + -0.3103333334)(x + -0.3103333334) = 0.06097344449

Calculate the square root of the right side: 0.246928015

Break this problem into two subproblems by setting 
(x + -0.3103333334) equal to 0.246928015 and -0.246928015.

Subproblem 1
x + -0.3103333334 = 0.246928015

Simplifying
x + -0.3103333334 = 0.246928015

Reorder the terms:
-0.3103333334 + x = 0.246928015

Solving
-0.3103333334 + x = 0.246928015

Solving for variable 'x'.

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

Add '0.3103333334' to each side of the equation.
-0.3103333334 + 0.3103333334 + x = 0.246928015 + 0.3103333334

Combine like terms: -0.3103333334 + 0.3103333334 = 0.0000000000
0.0000000000 + x = 0.246928015 + 0.3103333334
x = 0.246928015 + 0.3103333334

Combine like terms: 0.246928015 + 0.3103333334 = 0.5572613484
x = 0.5572613484

Simplifying
x = 0.5572613484

Subproblem 2
x + -0.3103333334 = -0.246928015

Simplifying
x + -0.3103333334 = -0.246928015

Reorder the terms:
-0.3103333334 + x = -0.246928015

Solving
-0.3103333334 + x = -0.246928015

Solving for variable 'x'.

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

Add '0.3103333334' to each side of the equation.
-0.3103333334 + 0.3103333334 + x = -0.246928015 + 0.3103333334

Combine like terms: -0.3103333334 + 0.3103333334 = 0.0000000000
0.0000000000 + x = -0.246928015 + 0.3103333334
x = -0.246928015 + 0.3103333334

Combine like terms: -0.246928015 + 0.3103333334 = 0.0634053184
x = 0.0634053184

Simplifying
x = 0.0634053184

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5572613484, 0.0634053184}