6x^2+29x-19=0

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Solution for 6x^2+29x-19=0 equation: 


Simplifying
6x2 + 29x + -19 = 0

Reorder the terms:
-19 + 29x + 6x2 = 0

Solving
-19 + 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'.
-3.166666667 + 4.833333333x + x2 = 0

Move the constant term to the right:

Add '3.166666667' to each side of the equation.
-3.166666667 + 4.833333333x + 3.166666667 + x2 = 0 + 3.166666667

Reorder the terms:
-3.166666667 + 3.166666667 + 4.833333333x + x2 = 0 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + 4.833333333x + x2 = 0 + 3.166666667
4.833333333x + x2 = 0 + 3.166666667

Combine like terms: 0 + 3.166666667 = 3.166666667
4.833333333x + x2 = 3.166666667

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 = 3.166666667 + 5.840277779

Reorder the terms:
5.840277779 + 4.833333333x + x2 = 3.166666667 + 5.840277779

Combine like terms: 3.166666667 + 5.840277779 = 9.006944446
5.840277779 + 4.833333333x + x2 = 9.006944446

Factor a perfect square on the left side:
(x + 2.416666667)(x + 2.416666667) = 9.006944446

Calculate the square root of the right side: 3.001157184

Break this problem into two subproblems by setting 
(x + 2.416666667) equal to 3.001157184 and -3.001157184.


Subproblem 1
x + 2.416666667 = 3.001157184

Simplifying
x + 2.416666667 = 3.001157184

Reorder the terms:
2.416666667 + x = 3.001157184

Solving
2.416666667 + x = 3.001157184

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 = 3.001157184 + -2.416666667

Combine like terms: 2.416666667 + -2.416666667 = 0.000000000
0.000000000 + x = 3.001157184 + -2.416666667
x = 3.001157184 + -2.416666667

Combine like terms: 3.001157184 + -2.416666667 = 0.584490517
x = 0.584490517

Simplifying
x = 0.584490517


Subproblem 2
x + 2.416666667 = -3.001157184

Simplifying
x + 2.416666667 = -3.001157184

Reorder the terms:
2.416666667 + x = -3.001157184

Solving
2.416666667 + x = -3.001157184

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 = -3.001157184 + -2.416666667

Combine like terms: 2.416666667 + -2.416666667 = 0.000000000
0.000000000 + x = -3.001157184 + -2.416666667
x = -3.001157184 + -2.416666667

Combine like terms: -3.001157184 + -2.416666667 = -5.417823851
x = -5.417823851

Simplifying
x = -5.417823851


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.584490517, -5.417823851}

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