6x^2-11x-24=0

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Solution for 6x^2-11x-24=0 equation: 


Simplifying
6x2 + -11x + -24 = 0

Reorder the terms:
-24 + -11x + 6x2 = 0

Solving
-24 + -11x + 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 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1.833333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -1.833333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1.833333333x + x2 = 0 + 4
-1.833333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1.833333333x + x2 = 4

The x term is -1.833333333x.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333x + 0.8402777775 + x2 = 4 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = 4 + 0.8402777775

Combine like terms: 4 + 0.8402777775 = 4.8402777775
0.8402777775 + -1.833333333x + x2 = 4.8402777775

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = 4.8402777775

Calculate the square root of the right side: 2.20006313

Break this problem into two subproblems by setting 
(x + -0.9166666665) equal to 2.20006313 and -2.20006313.


Subproblem 1
x + -0.9166666665 = 2.20006313

Simplifying
x + -0.9166666665 = 2.20006313

Reorder the terms:
-0.9166666665 + x = 2.20006313

Solving
-0.9166666665 + x = 2.20006313

Solving for variable 'x'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + x = 2.20006313 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = 2.20006313 + 0.9166666665
x = 2.20006313 + 0.9166666665

Combine like terms: 2.20006313 + 0.9166666665 = 3.1167297965
x = 3.1167297965

Simplifying
x = 3.1167297965


Subproblem 2
x + -0.9166666665 = -2.20006313

Simplifying
x + -0.9166666665 = -2.20006313

Reorder the terms:
-0.9166666665 + x = -2.20006313

Solving
-0.9166666665 + x = -2.20006313

Solving for variable 'x'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + x = -2.20006313 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = -2.20006313 + 0.9166666665
x = -2.20006313 + 0.9166666665

Combine like terms: -2.20006313 + 0.9166666665 = -1.2833964635
x = -1.2833964635

Simplifying
x = -1.2833964635


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.1167297965, -1.2833964635}

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