6x^2+29x-24=0

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Solution for 6x^2+29x-24=0 equation: 


Simplifying
6x2 + 29x + -24 = 0

Reorder the terms:
-24 + 29x + 6x2 = 0

Solving
-24 + 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'.
-4 + 4.833333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4.833333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 4.833333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4.833333333x + x2 = 0 + 4
4.833333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
4.833333333x + x2 = 4

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 = 4 + 5.840277779

Reorder the terms:
5.840277779 + 4.833333333x + x2 = 4 + 5.840277779

Combine like terms: 4 + 5.840277779 = 9.840277779
5.840277779 + 4.833333333x + x2 = 9.840277779

Factor a perfect square on the left side:
(x + 2.416666667)(x + 2.416666667) = 9.840277779

Calculate the square root of the right side: 3.136921704

Break this problem into two subproblems by setting 
(x + 2.416666667) equal to 3.136921704 and -3.136921704.


Subproblem 1
x + 2.416666667 = 3.136921704

Simplifying
x + 2.416666667 = 3.136921704

Reorder the terms:
2.416666667 + x = 3.136921704

Solving
2.416666667 + x = 3.136921704

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 = 3.136921704 + -2.416666667

Combine like terms: 2.416666667 + -2.416666667 = 0.000000000
0.000000000 + x = 3.136921704 + -2.416666667
x = 3.136921704 + -2.416666667

Combine like terms: 3.136921704 + -2.416666667 = 0.720255037
x = 0.720255037

Simplifying
x = 0.720255037


Subproblem 2
x + 2.416666667 = -3.136921704

Simplifying
x + 2.416666667 = -3.136921704

Reorder the terms:
2.416666667 + x = -3.136921704

Solving
2.416666667 + x = -3.136921704

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 = -3.136921704 + -2.416666667

Combine like terms: 2.416666667 + -2.416666667 = 0.000000000
0.000000000 + x = -3.136921704 + -2.416666667
x = -3.136921704 + -2.416666667

Combine like terms: -3.136921704 + -2.416666667 = -5.553588371
x = -5.553588371

Simplifying
x = -5.553588371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.720255037, -5.553588371}

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