3x^2-4.4x+1.3=0

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Solution for 3x^2-4.4x+1.3=0 equation: 


Simplifying
3x2 + -4.4x + 1.3 = 0

Reorder the terms:
1.3 + -4.4x + 3x2 = 0

Solving
1.3 + -4.4x + 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'.
0.4333333333 + -1.466666667x + x2 = 0

Move the constant term to the right:

Add '-0.4333333333' to each side of the equation.
0.4333333333 + -1.466666667x + -0.4333333333 + x2 = 0 + -0.4333333333

Reorder the terms:
0.4333333333 + -0.4333333333 + -1.466666667x + x2 = 0 + -0.4333333333

Combine like terms: 0.4333333333 + -0.4333333333 = 0.0000000000
0.0000000000 + -1.466666667x + x2 = 0 + -0.4333333333
-1.466666667x + x2 = 0 + -0.4333333333

Combine like terms: 0 + -0.4333333333 = -0.4333333333
-1.466666667x + x2 = -0.4333333333

The x term is -1.466666667x.  Take half its coefficient (-0.7333333335).
Square it (0.5377777780) and add it to both sides.

Add '0.5377777780' to each side of the equation.
-1.466666667x + 0.5377777780 + x2 = -0.4333333333 + 0.5377777780

Reorder the terms:
0.5377777780 + -1.466666667x + x2 = -0.4333333333 + 0.5377777780

Combine like terms: -0.4333333333 + 0.5377777780 = 0.1044444447
0.5377777780 + -1.466666667x + x2 = 0.1044444447

Factor a perfect square on the left side:
(x + -0.7333333335)(x + -0.7333333335) = 0.1044444447

Calculate the square root of the right side: 0.323178658

Break this problem into two subproblems by setting 
(x + -0.7333333335) equal to 0.323178658 and -0.323178658.


Subproblem 1
x + -0.7333333335 = 0.323178658

Simplifying
x + -0.7333333335 = 0.323178658

Reorder the terms:
-0.7333333335 + x = 0.323178658

Solving
-0.7333333335 + x = 0.323178658

Solving for variable 'x'.

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

Add '0.7333333335' to each side of the equation.
-0.7333333335 + 0.7333333335 + x = 0.323178658 + 0.7333333335

Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000
0.0000000000 + x = 0.323178658 + 0.7333333335
x = 0.323178658 + 0.7333333335

Combine like terms: 0.323178658 + 0.7333333335 = 1.0565119915
x = 1.0565119915

Simplifying
x = 1.0565119915


Subproblem 2
x + -0.7333333335 = -0.323178658

Simplifying
x + -0.7333333335 = -0.323178658

Reorder the terms:
-0.7333333335 + x = -0.323178658

Solving
-0.7333333335 + x = -0.323178658

Solving for variable 'x'.

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

Add '0.7333333335' to each side of the equation.
-0.7333333335 + 0.7333333335 + x = -0.323178658 + 0.7333333335

Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000
0.0000000000 + x = -0.323178658 + 0.7333333335
x = -0.323178658 + 0.7333333335

Combine like terms: -0.323178658 + 0.7333333335 = 0.4101546755
x = 0.4101546755

Simplifying
x = 0.4101546755


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0565119915, 0.4101546755}

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