(3x^2)-3.4x+0.16=0

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Solution for (3x^2)-3.4x+0.16=0 equation: 


Simplifying
(3x2) + -3.4x + 0.16 = 0

Reorder the terms:
0.16 + -3.4x + (3x2) = 0

Solving
0.16 + -3.4x + (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'.
0.05333333333 + -1.133333333x + x2 = 0

Move the constant term to the right:

Add '-0.05333333333' to each side of the equation.
0.05333333333 + -1.133333333x + -0.05333333333 + x2 = 0 + -0.05333333333

Reorder the terms:
0.05333333333 + -0.05333333333 + -1.133333333x + x2 = 0 + -0.05333333333

Combine like terms: 0.05333333333 + -0.05333333333 = 0.00000000000
0.00000000000 + -1.133333333x + x2 = 0 + -0.05333333333
-1.133333333x + x2 = 0 + -0.05333333333

Combine like terms: 0 + -0.05333333333 = -0.05333333333
-1.133333333x + x2 = -0.05333333333

The x term is -1.133333333x.  Take half its coefficient (-0.5666666665).
Square it (0.3211111109) and add it to both sides.

Add '0.3211111109' to each side of the equation.
-1.133333333x + 0.3211111109 + x2 = -0.05333333333 + 0.3211111109

Reorder the terms:
0.3211111109 + -1.133333333x + x2 = -0.05333333333 + 0.3211111109

Combine like terms: -0.05333333333 + 0.3211111109 = 0.26777777757
0.3211111109 + -1.133333333x + x2 = 0.26777777757

Factor a perfect square on the left side:
((x) + -0.5666666665)((x) + -0.5666666665) = 0.26777777757

Calculate the square root of the right side: 0.51747249

Break this problem into two subproblems by setting 
((x) + -0.5666666665) equal to 0.51747249 and -0.51747249.


Subproblem 1
(x) + -0.5666666665 = 0.51747249

Simplifying
(x) + -0.5666666665 = 0.51747249
x + -0.5666666665 = 0.51747249

Reorder the terms:
-0.5666666665 + x = 0.51747249

Solving
-0.5666666665 + x = 0.51747249

Solving for variable 'x'.

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

Add '0.5666666665' to each side of the equation.
-0.5666666665 + 0.5666666665 + x = 0.51747249 + 0.5666666665

Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000
0.0000000000 + x = 0.51747249 + 0.5666666665
x = 0.51747249 + 0.5666666665

Combine like terms: 0.51747249 + 0.5666666665 = 1.0841391565
x = 1.0841391565

Simplifying
x = 1.0841391565


Subproblem 2
(x) + -0.5666666665 = -0.51747249

Simplifying
(x) + -0.5666666665 = -0.51747249
x + -0.5666666665 = -0.51747249

Reorder the terms:
-0.5666666665 + x = -0.51747249

Solving
-0.5666666665 + x = -0.51747249

Solving for variable 'x'.

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

Add '0.5666666665' to each side of the equation.
-0.5666666665 + 0.5666666665 + x = -0.51747249 + 0.5666666665

Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000
0.0000000000 + x = -0.51747249 + 0.5666666665
x = -0.51747249 + 0.5666666665

Combine like terms: -0.51747249 + 0.5666666665 = 0.0491941765
x = 0.0491941765

Simplifying
x = 0.0491941765


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0841391565, 0.0491941765}

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