3x^2-55x+146=0

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Solution for 3x^2-55x+146=0 equation: 


Simplifying
3x2 + -55x + 146 = 0

Reorder the terms:
146 + -55x + 3x2 = 0

Solving
146 + -55x + 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'.
48.66666667 + -18.33333333x + x2 = 0

Move the constant term to the right:

Add '-48.66666667' to each side of the equation.
48.66666667 + -18.33333333x + -48.66666667 + x2 = 0 + -48.66666667

Reorder the terms:
48.66666667 + -48.66666667 + -18.33333333x + x2 = 0 + -48.66666667

Combine like terms: 48.66666667 + -48.66666667 = 0.00000000
0.00000000 + -18.33333333x + x2 = 0 + -48.66666667
-18.33333333x + x2 = 0 + -48.66666667

Combine like terms: 0 + -48.66666667 = -48.66666667
-18.33333333x + x2 = -48.66666667

The x term is -18.33333333x.  Take half its coefficient (-9.166666665).
Square it (84.02777775) and add it to both sides.

Add '84.02777775' to each side of the equation.
-18.33333333x + 84.02777775 + x2 = -48.66666667 + 84.02777775

Reorder the terms:
84.02777775 + -18.33333333x + x2 = -48.66666667 + 84.02777775

Combine like terms: -48.66666667 + 84.02777775 = 35.36111108
84.02777775 + -18.33333333x + x2 = 35.36111108

Factor a perfect square on the left side:
(x + -9.166666665)(x + -9.166666665) = 35.36111108

Calculate the square root of the right side: 5.946520922

Break this problem into two subproblems by setting 
(x + -9.166666665) equal to 5.946520922 and -5.946520922.


Subproblem 1
x + -9.166666665 = 5.946520922

Simplifying
x + -9.166666665 = 5.946520922

Reorder the terms:
-9.166666665 + x = 5.946520922

Solving
-9.166666665 + x = 5.946520922

Solving for variable 'x'.

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

Add '9.166666665' to each side of the equation.
-9.166666665 + 9.166666665 + x = 5.946520922 + 9.166666665

Combine like terms: -9.166666665 + 9.166666665 = 0.000000000
0.000000000 + x = 5.946520922 + 9.166666665
x = 5.946520922 + 9.166666665

Combine like terms: 5.946520922 + 9.166666665 = 15.113187587
x = 15.113187587

Simplifying
x = 15.113187587


Subproblem 2
x + -9.166666665 = -5.946520922

Simplifying
x + -9.166666665 = -5.946520922

Reorder the terms:
-9.166666665 + x = -5.946520922

Solving
-9.166666665 + x = -5.946520922

Solving for variable 'x'.

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

Add '9.166666665' to each side of the equation.
-9.166666665 + 9.166666665 + x = -5.946520922 + 9.166666665

Combine like terms: -9.166666665 + 9.166666665 = 0.000000000
0.000000000 + x = -5.946520922 + 9.166666665
x = -5.946520922 + 9.166666665

Combine like terms: -5.946520922 + 9.166666665 = 3.220145743
x = 3.220145743

Simplifying
x = 3.220145743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.113187587, 3.220145743}

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