3x^2-40x+36=0

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Solution for 3x^2-40x+36=0 equation: 


Simplifying
3x2 + -40x + 36 = 0

Reorder the terms:
36 + -40x + 3x2 = 0

Solving
36 + -40x + 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'.
12 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -13.33333333x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -13.33333333x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -13.33333333x + x2 = 0 + -12
-13.33333333x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-13.33333333x + x2 = -12

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = -12 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = -12 + 44.44444442

Combine like terms: -12 + 44.44444442 = 32.44444442
44.44444442 + -13.33333333x + x2 = 32.44444442

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 32.44444442

Calculate the square root of the right side: 5.696002495

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 5.696002495 and -5.696002495.


Subproblem 1
x + -6.666666665 = 5.696002495

Simplifying
x + -6.666666665 = 5.696002495

Reorder the terms:
-6.666666665 + x = 5.696002495

Solving
-6.666666665 + x = 5.696002495

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 5.696002495 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 5.696002495 + 6.666666665
x = 5.696002495 + 6.666666665

Combine like terms: 5.696002495 + 6.666666665 = 12.36266916
x = 12.36266916

Simplifying
x = 12.36266916


Subproblem 2
x + -6.666666665 = -5.696002495

Simplifying
x + -6.666666665 = -5.696002495

Reorder the terms:
-6.666666665 + x = -5.696002495

Solving
-6.666666665 + x = -5.696002495

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -5.696002495 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -5.696002495 + 6.666666665
x = -5.696002495 + 6.666666665

Combine like terms: -5.696002495 + 6.666666665 = 0.97066417
x = 0.97066417

Simplifying
x = 0.97066417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.36266916, 0.97066417}

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