6x^2-35x-9=0

Solution for 6x^2-35x-9=0 equation:

Simplifying
6x2 + -35x + -9 = 0

Reorder the terms:
-9 + -35x + 6x2 = 0

Solving
-9 + -35x + 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'.
-1.5 + -5.833333333x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -5.833333333x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -5.833333333x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -5.833333333x + x2 = 0 + 1.5
-5.833333333x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-5.833333333x + x2 = 1.5

The x term is -5.833333333x.  Take half its coefficient (-2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
-5.833333333x + 8.506944446 + x2 = 1.5 + 8.506944446

Reorder the terms:
8.506944446 + -5.833333333x + x2 = 1.5 + 8.506944446

Combine like terms: 1.5 + 8.506944446 = 10.006944446
8.506944446 + -5.833333333x + x2 = 10.006944446

Factor a perfect square on the left side:
(x + -2.916666667)(x + -2.916666667) = 10.006944446

Calculate the square root of the right side: 3.163375483

Break this problem into two subproblems by setting 
(x + -2.916666667) equal to 3.163375483 and -3.163375483.

Subproblem 1
x + -2.916666667 = 3.163375483

Simplifying
x + -2.916666667 = 3.163375483

Reorder the terms:
-2.916666667 + x = 3.163375483

Solving
-2.916666667 + x = 3.163375483

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = 3.163375483 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = 3.163375483 + 2.916666667
x = 3.163375483 + 2.916666667

Combine like terms: 3.163375483 + 2.916666667 = 6.08004215
x = 6.08004215

Simplifying
x = 6.08004215

Subproblem 2
x + -2.916666667 = -3.163375483

Simplifying
x + -2.916666667 = -3.163375483

Reorder the terms:
-2.916666667 + x = -3.163375483

Solving
-2.916666667 + x = -3.163375483

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = -3.163375483 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = -3.163375483 + 2.916666667
x = -3.163375483 + 2.916666667

Combine like terms: -3.163375483 + 2.916666667 = -0.246708816
x = -0.246708816

Simplifying
x = -0.246708816

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.08004215, -0.246708816}