6x^2+215x+308=0

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Solution for 6x^2+215x+308=0 equation: 


Simplifying
6x2 + 215x + 308 = 0

Reorder the terms:
308 + 215x + 6x2 = 0

Solving
308 + 215x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
51.33333333 + 35.83333333x + x2 = 0

Move the constant term to the right:

Add '-51.33333333' to each side of the equation.
51.33333333 + 35.83333333x + -51.33333333 + x2 = 0 + -51.33333333

Reorder the terms:
51.33333333 + -51.33333333 + 35.83333333x + x2 = 0 + -51.33333333

Combine like terms: 51.33333333 + -51.33333333 = 0.00000000
0.00000000 + 35.83333333x + x2 = 0 + -51.33333333
35.83333333x + x2 = 0 + -51.33333333

Combine like terms: 0 + -51.33333333 = -51.33333333
35.83333333x + x2 = -51.33333333

The x term is 35.83333333x.  Take half its coefficient (17.91666667).
Square it (321.0069446) and add it to both sides.

Add '321.0069446' to each side of the equation.
35.83333333x + 321.0069446 + x2 = -51.33333333 + 321.0069446

Reorder the terms:
321.0069446 + 35.83333333x + x2 = -51.33333333 + 321.0069446

Combine like terms: -51.33333333 + 321.0069446 = 269.67361127
321.0069446 + 35.83333333x + x2 = 269.67361127

Factor a perfect square on the left side:
(x + 17.91666667)(x + 17.91666667) = 269.67361127

Calculate the square root of the right side: 16.421742029

Break this problem into two subproblems by setting 
(x + 17.91666667) equal to 16.421742029 and -16.421742029.


Subproblem 1
x + 17.91666667 = 16.421742029

Simplifying
x + 17.91666667 = 16.421742029

Reorder the terms:
17.91666667 + x = 16.421742029

Solving
17.91666667 + x = 16.421742029

Solving for variable 'x'.

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

Add '-17.91666667' to each side of the equation.
17.91666667 + -17.91666667 + x = 16.421742029 + -17.91666667

Combine like terms: 17.91666667 + -17.91666667 = 0.00000000
0.00000000 + x = 16.421742029 + -17.91666667
x = 16.421742029 + -17.91666667

Combine like terms: 16.421742029 + -17.91666667 = -1.494924641
x = -1.494924641

Simplifying
x = -1.494924641


Subproblem 2
x + 17.91666667 = -16.421742029

Simplifying
x + 17.91666667 = -16.421742029

Reorder the terms:
17.91666667 + x = -16.421742029

Solving
17.91666667 + x = -16.421742029

Solving for variable 'x'.

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

Add '-17.91666667' to each side of the equation.
17.91666667 + -17.91666667 + x = -16.421742029 + -17.91666667

Combine like terms: 17.91666667 + -17.91666667 = 0.00000000
0.00000000 + x = -16.421742029 + -17.91666667
x = -16.421742029 + -17.91666667

Combine like terms: -16.421742029 + -17.91666667 = -34.338408699
x = -34.338408699

Simplifying
x = -34.338408699


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.494924641, -34.338408699}

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