3*x^2-85*x-316=0

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Solution for 3*x^2-85*x-316=0 equation: 


Simplifying
3x2 + -85x + -316 = 0

Reorder the terms:
-316 + -85x + 3x2 = 0

Solving
-316 + -85x + 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'.
-105.3333333 + -28.33333333x + x2 = 0

Move the constant term to the right:

Add '105.3333333' to each side of the equation.
-105.3333333 + -28.33333333x + 105.3333333 + x2 = 0 + 105.3333333

Reorder the terms:
-105.3333333 + 105.3333333 + -28.33333333x + x2 = 0 + 105.3333333

Combine like terms: -105.3333333 + 105.3333333 = 0.0000000
0.0000000 + -28.33333333x + x2 = 0 + 105.3333333
-28.33333333x + x2 = 0 + 105.3333333

Combine like terms: 0 + 105.3333333 = 105.3333333
-28.33333333x + x2 = 105.3333333

The x term is -28.33333333x.  Take half its coefficient (-14.16666667).
Square it (200.6944445) and add it to both sides.

Add '200.6944445' to each side of the equation.
-28.33333333x + 200.6944445 + x2 = 105.3333333 + 200.6944445

Reorder the terms:
200.6944445 + -28.33333333x + x2 = 105.3333333 + 200.6944445

Combine like terms: 105.3333333 + 200.6944445 = 306.0277778
200.6944445 + -28.33333333x + x2 = 306.0277778

Factor a perfect square on the left side:
(x + -14.16666667)(x + -14.16666667) = 306.0277778

Calculate the square root of the right side: 17.493649642

Break this problem into two subproblems by setting 
(x + -14.16666667) equal to 17.493649642 and -17.493649642.


Subproblem 1
x + -14.16666667 = 17.493649642

Simplifying
x + -14.16666667 = 17.493649642

Reorder the terms:
-14.16666667 + x = 17.493649642

Solving
-14.16666667 + x = 17.493649642

Solving for variable 'x'.

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

Add '14.16666667' to each side of the equation.
-14.16666667 + 14.16666667 + x = 17.493649642 + 14.16666667

Combine like terms: -14.16666667 + 14.16666667 = 0.00000000
0.00000000 + x = 17.493649642 + 14.16666667
x = 17.493649642 + 14.16666667

Combine like terms: 17.493649642 + 14.16666667 = 31.660316312
x = 31.660316312

Simplifying
x = 31.660316312


Subproblem 2
x + -14.16666667 = -17.493649642

Simplifying
x + -14.16666667 = -17.493649642

Reorder the terms:
-14.16666667 + x = -17.493649642

Solving
-14.16666667 + x = -17.493649642

Solving for variable 'x'.

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

Add '14.16666667' to each side of the equation.
-14.16666667 + 14.16666667 + x = -17.493649642 + 14.16666667

Combine like terms: -14.16666667 + 14.16666667 = 0.00000000
0.00000000 + x = -17.493649642 + 14.16666667
x = -17.493649642 + 14.16666667

Combine like terms: -17.493649642 + 14.16666667 = -3.326982972
x = -3.326982972

Simplifying
x = -3.326982972


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.660316312, -3.326982972}

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