3x^2-38x+32=0

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Solution for 3x^2-38x+32=0 equation: 


Simplifying
3x2 + -38x + 32 = 0

Reorder the terms:
32 + -38x + 3x2 = 0

Solving
32 + -38x + 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'.
10.66666667 + -12.66666667x + x2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + -12.66666667x + -10.66666667 + x2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + -12.66666667x + x2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + -12.66666667x + x2 = 0 + -10.66666667
-12.66666667x + x2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
-12.66666667x + x2 = -10.66666667

The x term is -12.66666667x.  Take half its coefficient (-6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
-12.66666667x + 40.11111113 + x2 = -10.66666667 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667x + x2 = -10.66666667 + 40.11111113

Combine like terms: -10.66666667 + 40.11111113 = 29.44444446
40.11111113 + -12.66666667x + x2 = 29.44444446

Factor a perfect square on the left side:
(x + -6.333333335)(x + -6.333333335) = 29.44444446

Calculate the square root of the right side: 5.426273533

Break this problem into two subproblems by setting 
(x + -6.333333335) equal to 5.426273533 and -5.426273533.


Subproblem 1
x + -6.333333335 = 5.426273533

Simplifying
x + -6.333333335 = 5.426273533

Reorder the terms:
-6.333333335 + x = 5.426273533

Solving
-6.333333335 + x = 5.426273533

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = 5.426273533 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = 5.426273533 + 6.333333335
x = 5.426273533 + 6.333333335

Combine like terms: 5.426273533 + 6.333333335 = 11.759606868
x = 11.759606868

Simplifying
x = 11.759606868


Subproblem 2
x + -6.333333335 = -5.426273533

Simplifying
x + -6.333333335 = -5.426273533

Reorder the terms:
-6.333333335 + x = -5.426273533

Solving
-6.333333335 + x = -5.426273533

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = -5.426273533 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = -5.426273533 + 6.333333335
x = -5.426273533 + 6.333333335

Combine like terms: -5.426273533 + 6.333333335 = 0.907059802
x = 0.907059802

Simplifying
x = 0.907059802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.759606868, 0.907059802}

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