3*x^2-85*x-79=0

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Solution for 3*x^2-85*x-79=0 equation: 


Simplifying
3x2 + -85x + -79 = 0

Reorder the terms:
-79 + -85x + 3x2 = 0

Solving
-79 + -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'.
-26.33333333 + -28.33333333x + x2 = 0

Move the constant term to the right:

Add '26.33333333' to each side of the equation.
-26.33333333 + -28.33333333x + 26.33333333 + x2 = 0 + 26.33333333

Reorder the terms:
-26.33333333 + 26.33333333 + -28.33333333x + x2 = 0 + 26.33333333

Combine like terms: -26.33333333 + 26.33333333 = 0.00000000
0.00000000 + -28.33333333x + x2 = 0 + 26.33333333
-28.33333333x + x2 = 0 + 26.33333333

Combine like terms: 0 + 26.33333333 = 26.33333333
-28.33333333x + x2 = 26.33333333

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 = 26.33333333 + 200.6944445

Reorder the terms:
200.6944445 + -28.33333333x + x2 = 26.33333333 + 200.6944445

Combine like terms: 26.33333333 + 200.6944445 = 227.02777783
200.6944445 + -28.33333333x + x2 = 227.02777783

Factor a perfect square on the left side:
(x + -14.16666667)(x + -14.16666667) = 227.02777783

Calculate the square root of the right side: 15.067440985

Break this problem into two subproblems by setting 
(x + -14.16666667) equal to 15.067440985 and -15.067440985.


Subproblem 1
x + -14.16666667 = 15.067440985

Simplifying
x + -14.16666667 = 15.067440985

Reorder the terms:
-14.16666667 + x = 15.067440985

Solving
-14.16666667 + x = 15.067440985

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 = 15.067440985 + 14.16666667

Combine like terms: -14.16666667 + 14.16666667 = 0.00000000
0.00000000 + x = 15.067440985 + 14.16666667
x = 15.067440985 + 14.16666667

Combine like terms: 15.067440985 + 14.16666667 = 29.234107655
x = 29.234107655

Simplifying
x = 29.234107655


Subproblem 2
x + -14.16666667 = -15.067440985

Simplifying
x + -14.16666667 = -15.067440985

Reorder the terms:
-14.16666667 + x = -15.067440985

Solving
-14.16666667 + x = -15.067440985

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 = -15.067440985 + 14.16666667

Combine like terms: -14.16666667 + 14.16666667 = 0.00000000
0.00000000 + x = -15.067440985 + 14.16666667
x = -15.067440985 + 14.16666667

Combine like terms: -15.067440985 + 14.16666667 = -0.900774315
x = -0.900774315

Simplifying
x = -0.900774315


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.234107655, -0.900774315}

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