3x^2-41x+59=0

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Solution for 3x^2-41x+59=0 equation: 


Simplifying
3x2 + -41x + 59 = 0

Reorder the terms:
59 + -41x + 3x2 = 0

Solving
59 + -41x + 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'.
19.66666667 + -13.66666667x + x2 = 0

Move the constant term to the right:

Add '-19.66666667' to each side of the equation.
19.66666667 + -13.66666667x + -19.66666667 + x2 = 0 + -19.66666667

Reorder the terms:
19.66666667 + -19.66666667 + -13.66666667x + x2 = 0 + -19.66666667

Combine like terms: 19.66666667 + -19.66666667 = 0.00000000
0.00000000 + -13.66666667x + x2 = 0 + -19.66666667
-13.66666667x + x2 = 0 + -19.66666667

Combine like terms: 0 + -19.66666667 = -19.66666667
-13.66666667x + x2 = -19.66666667

The x term is -13.66666667x.  Take half its coefficient (-6.833333335).
Square it (46.69444447) and add it to both sides.

Add '46.69444447' to each side of the equation.
-13.66666667x + 46.69444447 + x2 = -19.66666667 + 46.69444447

Reorder the terms:
46.69444447 + -13.66666667x + x2 = -19.66666667 + 46.69444447

Combine like terms: -19.66666667 + 46.69444447 = 27.0277778
46.69444447 + -13.66666667x + x2 = 27.0277778

Factor a perfect square on the left side:
(x + -6.833333335)(x + -6.833333335) = 27.0277778

Calculate the square root of the right side: 5.198824656

Break this problem into two subproblems by setting 
(x + -6.833333335) equal to 5.198824656 and -5.198824656.


Subproblem 1
x + -6.833333335 = 5.198824656

Simplifying
x + -6.833333335 = 5.198824656

Reorder the terms:
-6.833333335 + x = 5.198824656

Solving
-6.833333335 + x = 5.198824656

Solving for variable 'x'.

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

Add '6.833333335' to each side of the equation.
-6.833333335 + 6.833333335 + x = 5.198824656 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + x = 5.198824656 + 6.833333335
x = 5.198824656 + 6.833333335

Combine like terms: 5.198824656 + 6.833333335 = 12.032157991
x = 12.032157991

Simplifying
x = 12.032157991


Subproblem 2
x + -6.833333335 = -5.198824656

Simplifying
x + -6.833333335 = -5.198824656

Reorder the terms:
-6.833333335 + x = -5.198824656

Solving
-6.833333335 + x = -5.198824656

Solving for variable 'x'.

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

Add '6.833333335' to each side of the equation.
-6.833333335 + 6.833333335 + x = -5.198824656 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + x = -5.198824656 + 6.833333335
x = -5.198824656 + 6.833333335

Combine like terms: -5.198824656 + 6.833333335 = 1.634508679
x = 1.634508679

Simplifying
x = 1.634508679


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.032157991, 1.634508679}

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