6x^2-29x-9=0

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Solution for 6x^2-29x-9=0 equation: 


Simplifying
6x2 + -29x + -9 = 0

Reorder the terms:
-9 + -29x + 6x2 = 0

Solving
-9 + -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'.
-1.5 + -4.833333333x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -4.833333333x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -4.833333333x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -4.833333333x + x2 = 0 + 1.5
-4.833333333x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-4.833333333x + x2 = 1.5

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 + 5.840277779

Reorder the terms:
5.840277779 + -4.833333333x + x2 = 1.5 + 5.840277779

Combine like terms: 1.5 + 5.840277779 = 7.340277779
5.840277779 + -4.833333333x + x2 = 7.340277779

Factor a perfect square on the left side:
(x + -2.416666667)(x + -2.416666667) = 7.340277779

Calculate the square root of the right side: 2.709294701

Break this problem into two subproblems by setting 
(x + -2.416666667) equal to 2.709294701 and -2.709294701.


Subproblem 1
x + -2.416666667 = 2.709294701

Simplifying
x + -2.416666667 = 2.709294701

Reorder the terms:
-2.416666667 + x = 2.709294701

Solving
-2.416666667 + x = 2.709294701

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 = 2.709294701 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = 2.709294701 + 2.416666667
x = 2.709294701 + 2.416666667

Combine like terms: 2.709294701 + 2.416666667 = 5.125961368
x = 5.125961368

Simplifying
x = 5.125961368


Subproblem 2
x + -2.416666667 = -2.709294701

Simplifying
x + -2.416666667 = -2.709294701

Reorder the terms:
-2.416666667 + x = -2.709294701

Solving
-2.416666667 + x = -2.709294701

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 = -2.709294701 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = -2.709294701 + 2.416666667
x = -2.709294701 + 2.416666667

Combine like terms: -2.709294701 + 2.416666667 = -0.292628034
x = -0.292628034

Simplifying
x = -0.292628034


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.125961368, -0.292628034}

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