3x^2-19x-92=0

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Solution for 3x^2-19x-92=0 equation: 


Simplifying
3x2 + -19x + -92 = 0

Reorder the terms:
-92 + -19x + 3x2 = 0

Solving
-92 + -19x + 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'.
-30.66666667 + -6.333333333x + x2 = 0

Move the constant term to the right:

Add '30.66666667' to each side of the equation.
-30.66666667 + -6.333333333x + 30.66666667 + x2 = 0 + 30.66666667

Reorder the terms:
-30.66666667 + 30.66666667 + -6.333333333x + x2 = 0 + 30.66666667

Combine like terms: -30.66666667 + 30.66666667 = 0.00000000
0.00000000 + -6.333333333x + x2 = 0 + 30.66666667
-6.333333333x + x2 = 0 + 30.66666667

Combine like terms: 0 + 30.66666667 = 30.66666667
-6.333333333x + x2 = 30.66666667

The x term is -6.333333333x.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x + 10.02777778 + x2 = 30.66666667 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x + x2 = 30.66666667 + 10.02777778

Combine like terms: 30.66666667 + 10.02777778 = 40.69444445
10.02777778 + -6.333333333x + x2 = 40.69444445

Factor a perfect square on the left side:
(x + -3.166666667)(x + -3.166666667) = 40.69444445

Calculate the square root of the right side: 6.379219737

Break this problem into two subproblems by setting 
(x + -3.166666667) equal to 6.379219737 and -6.379219737.


Subproblem 1
x + -3.166666667 = 6.379219737

Simplifying
x + -3.166666667 = 6.379219737

Reorder the terms:
-3.166666667 + x = 6.379219737

Solving
-3.166666667 + x = 6.379219737

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = 6.379219737 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = 6.379219737 + 3.166666667
x = 6.379219737 + 3.166666667

Combine like terms: 6.379219737 + 3.166666667 = 9.545886404
x = 9.545886404

Simplifying
x = 9.545886404


Subproblem 2
x + -3.166666667 = -6.379219737

Simplifying
x + -3.166666667 = -6.379219737

Reorder the terms:
-3.166666667 + x = -6.379219737

Solving
-3.166666667 + x = -6.379219737

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = -6.379219737 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = -6.379219737 + 3.166666667
x = -6.379219737 + 3.166666667

Combine like terms: -6.379219737 + 3.166666667 = -3.21255307
x = -3.21255307

Simplifying
x = -3.21255307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.545886404, -3.21255307}

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