6x^2-29x-6=0

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Solution for 6x^2-29x-6=0 equation: 


Simplifying
6x2 + -29x + -6 = 0

Reorder the terms:
-6 + -29x + 6x2 = 0

Solving
-6 + -29x + 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 + -4.833333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.833333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.833333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.833333333x + x2 = 0 + 1
-4.833333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.833333333x + x2 = 1

The x term is -4.833333333x.  Take half its coefficient (-2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
-4.833333333x + 5.840277779 + x2 = 1 + 5.840277779

Reorder the terms:
5.840277779 + -4.833333333x + x2 = 1 + 5.840277779

Combine like terms: 1 + 5.840277779 = 6.840277779
5.840277779 + -4.833333333x + x2 = 6.840277779

Factor a perfect square on the left side:
(x + -2.416666667)(x + -2.416666667) = 6.840277779

Calculate the square root of the right side: 2.615392471

Break this problem into two subproblems by setting 
(x + -2.416666667) equal to 2.615392471 and -2.615392471.


Subproblem 1
x + -2.416666667 = 2.615392471

Simplifying
x + -2.416666667 = 2.615392471

Reorder the terms:
-2.416666667 + x = 2.615392471

Solving
-2.416666667 + x = 2.615392471

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = 2.615392471 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = 2.615392471 + 2.416666667
x = 2.615392471 + 2.416666667

Combine like terms: 2.615392471 + 2.416666667 = 5.032059138
x = 5.032059138

Simplifying
x = 5.032059138


Subproblem 2
x + -2.416666667 = -2.615392471

Simplifying
x + -2.416666667 = -2.615392471

Reorder the terms:
-2.416666667 + x = -2.615392471

Solving
-2.416666667 + x = -2.615392471

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = -2.615392471 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = -2.615392471 + 2.416666667
x = -2.615392471 + 2.416666667

Combine like terms: -2.615392471 + 2.416666667 = -0.198725804
x = -0.198725804

Simplifying
x = -0.198725804


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.032059138, -0.198725804}

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