3x^2-41x+46=0

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Solution for 3x^2-41x+46=0 equation: 


Simplifying
3x2 + -41x + 46 = 0

Reorder the terms:
46 + -41x + 3x2 = 0

Solving
46 + -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'.
15.33333333 + -13.66666667x + x2 = 0

Move the constant term to the right:

Add '-15.33333333' to each side of the equation.
15.33333333 + -13.66666667x + -15.33333333 + x2 = 0 + -15.33333333

Reorder the terms:
15.33333333 + -15.33333333 + -13.66666667x + x2 = 0 + -15.33333333

Combine like terms: 15.33333333 + -15.33333333 = 0.00000000
0.00000000 + -13.66666667x + x2 = 0 + -15.33333333
-13.66666667x + x2 = 0 + -15.33333333

Combine like terms: 0 + -15.33333333 = -15.33333333
-13.66666667x + x2 = -15.33333333

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 = -15.33333333 + 46.69444447

Reorder the terms:
46.69444447 + -13.66666667x + x2 = -15.33333333 + 46.69444447

Combine like terms: -15.33333333 + 46.69444447 = 31.36111114
46.69444447 + -13.66666667x + x2 = 31.36111114

Factor a perfect square on the left side:
(x + -6.833333335)(x + -6.833333335) = 31.36111114

Calculate the square root of the right side: 5.600099208

Break this problem into two subproblems by setting 
(x + -6.833333335) equal to 5.600099208 and -5.600099208.


Subproblem 1
x + -6.833333335 = 5.600099208

Simplifying
x + -6.833333335 = 5.600099208

Reorder the terms:
-6.833333335 + x = 5.600099208

Solving
-6.833333335 + x = 5.600099208

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 = 5.600099208 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + x = 5.600099208 + 6.833333335
x = 5.600099208 + 6.833333335

Combine like terms: 5.600099208 + 6.833333335 = 12.433432543
x = 12.433432543

Simplifying
x = 12.433432543


Subproblem 2
x + -6.833333335 = -5.600099208

Simplifying
x + -6.833333335 = -5.600099208

Reorder the terms:
-6.833333335 + x = -5.600099208

Solving
-6.833333335 + x = -5.600099208

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 = -5.600099208 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + x = -5.600099208 + 6.833333335
x = -5.600099208 + 6.833333335

Combine like terms: -5.600099208 + 6.833333335 = 1.233234127
x = 1.233234127

Simplifying
x = 1.233234127


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.433432543, 1.233234127}

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