3x^2-44x+40=0

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Solution for 3x^2-44x+40=0 equation: 


Simplifying
3x2 + -44x + 40 = 0

Reorder the terms:
40 + -44x + 3x2 = 0

Solving
40 + -44x + 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'.
13.33333333 + -14.66666667x + x2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + -14.66666667x + -13.33333333 + x2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + -14.66666667x + x2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + -14.66666667x + x2 = 0 + -13.33333333
-14.66666667x + x2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
-14.66666667x + x2 = -13.33333333

The x term is -14.66666667x.  Take half its coefficient (-7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
-14.66666667x + 53.77777780 + x2 = -13.33333333 + 53.77777780

Reorder the terms:
53.77777780 + -14.66666667x + x2 = -13.33333333 + 53.77777780

Combine like terms: -13.33333333 + 53.77777780 = 40.44444447
53.77777780 + -14.66666667x + x2 = 40.44444447

Factor a perfect square on the left side:
(x + -7.333333335)(x + -7.333333335) = 40.44444447

Calculate the square root of the right side: 6.359594678

Break this problem into two subproblems by setting 
(x + -7.333333335) equal to 6.359594678 and -6.359594678.


Subproblem 1
x + -7.333333335 = 6.359594678

Simplifying
x + -7.333333335 = 6.359594678

Reorder the terms:
-7.333333335 + x = 6.359594678

Solving
-7.333333335 + x = 6.359594678

Solving for variable 'x'.

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

Add '7.333333335' to each side of the equation.
-7.333333335 + 7.333333335 + x = 6.359594678 + 7.333333335

Combine like terms: -7.333333335 + 7.333333335 = 0.000000000
0.000000000 + x = 6.359594678 + 7.333333335
x = 6.359594678 + 7.333333335

Combine like terms: 6.359594678 + 7.333333335 = 13.692928013
x = 13.692928013

Simplifying
x = 13.692928013


Subproblem 2
x + -7.333333335 = -6.359594678

Simplifying
x + -7.333333335 = -6.359594678

Reorder the terms:
-7.333333335 + x = -6.359594678

Solving
-7.333333335 + x = -6.359594678

Solving for variable 'x'.

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

Add '7.333333335' to each side of the equation.
-7.333333335 + 7.333333335 + x = -6.359594678 + 7.333333335

Combine like terms: -7.333333335 + 7.333333335 = 0.000000000
0.000000000 + x = -6.359594678 + 7.333333335
x = -6.359594678 + 7.333333335

Combine like terms: -6.359594678 + 7.333333335 = 0.973738657
x = 0.973738657

Simplifying
x = 0.973738657


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.692928013, 0.973738657}

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