3x^2-35x-19-9=0

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Solution for 3x^2-35x-19-9=0 equation: 


Simplifying
3x2 + -35x + -19 + -9 = 0

Reorder the terms:
-19 + -9 + -35x + 3x2 = 0

Combine like terms: -19 + -9 = -28
-28 + -35x + 3x2 = 0

Solving
-28 + -35x + 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'.
-9.333333333 + -11.66666667x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + -11.66666667x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + -11.66666667x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + -11.66666667x + x2 = 0 + 9.333333333
-11.66666667x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
-11.66666667x + x2 = 9.333333333

The x term is -11.66666667x.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667x + 34.02777780 + x2 = 9.333333333 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667x + x2 = 9.333333333 + 34.02777780

Combine like terms: 9.333333333 + 34.02777780 = 43.361111133
34.02777780 + -11.66666667x + x2 = 43.361111133

Factor a perfect square on the left side:
(x + -5.833333335)(x + -5.833333335) = 43.361111133

Calculate the square root of the right side: 6.584915423

Break this problem into two subproblems by setting 
(x + -5.833333335) equal to 6.584915423 and -6.584915423.


Subproblem 1
x + -5.833333335 = 6.584915423

Simplifying
x + -5.833333335 = 6.584915423

Reorder the terms:
-5.833333335 + x = 6.584915423

Solving
-5.833333335 + x = 6.584915423

Solving for variable 'x'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = 6.584915423 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = 6.584915423 + 5.833333335
x = 6.584915423 + 5.833333335

Combine like terms: 6.584915423 + 5.833333335 = 12.418248758
x = 12.418248758

Simplifying
x = 12.418248758


Subproblem 2
x + -5.833333335 = -6.584915423

Simplifying
x + -5.833333335 = -6.584915423

Reorder the terms:
-5.833333335 + x = -6.584915423

Solving
-5.833333335 + x = -6.584915423

Solving for variable 'x'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = -6.584915423 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = -6.584915423 + 5.833333335
x = -6.584915423 + 5.833333335

Combine like terms: -6.584915423 + 5.833333335 = -0.751582088
x = -0.751582088

Simplifying
x = -0.751582088


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.418248758, -0.751582088}

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