3x^2-35x-5=0

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Solution for 3x^2-35x-5=0 equation: 


Simplifying
3x2 + -35x + -5 = 0

Reorder the terms:
-5 + -35x + 3x2 = 0

Solving
-5 + -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'.
-1.666666667 + -11.66666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -11.66666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -11.66666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -11.66666667x + x2 = 0 + 1.666666667
-11.66666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-11.66666667x + x2 = 1.666666667

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 = 1.666666667 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667x + x2 = 1.666666667 + 34.02777780

Combine like terms: 1.666666667 + 34.02777780 = 35.694444467
34.02777780 + -11.66666667x + x2 = 35.694444467

Factor a perfect square on the left side:
(x + -5.833333335)(x + -5.833333335) = 35.694444467

Calculate the square root of the right side: 5.974482778

Break this problem into two subproblems by setting 
(x + -5.833333335) equal to 5.974482778 and -5.974482778.


Subproblem 1
x + -5.833333335 = 5.974482778

Simplifying
x + -5.833333335 = 5.974482778

Reorder the terms:
-5.833333335 + x = 5.974482778

Solving
-5.833333335 + x = 5.974482778

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 = 5.974482778 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = 5.974482778 + 5.833333335
x = 5.974482778 + 5.833333335

Combine like terms: 5.974482778 + 5.833333335 = 11.807816113
x = 11.807816113

Simplifying
x = 11.807816113


Subproblem 2
x + -5.833333335 = -5.974482778

Simplifying
x + -5.833333335 = -5.974482778

Reorder the terms:
-5.833333335 + x = -5.974482778

Solving
-5.833333335 + x = -5.974482778

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 = -5.974482778 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = -5.974482778 + 5.833333335
x = -5.974482778 + 5.833333335

Combine like terms: -5.974482778 + 5.833333335 = -0.141149443
x = -0.141149443

Simplifying
x = -0.141149443


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.807816113, -0.141149443}

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