6x^2-11x-8=0

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Solution for 6x^2-11x-8=0 equation:


Simplifying
6x2 + -11x + -8 = 0

Reorder the terms:
-8 + -11x + 6x2 = 0

Solving
-8 + -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'.
-1.333333333 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1.833333333x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1.833333333x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1.833333333x + x2 = 0 + 1.333333333
-1.833333333x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1.833333333x + x2 = 1.333333333

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 = 1.333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = 1.333333333 + 0.8402777775

Combine like terms: 1.333333333 + 0.8402777775 = 2.1736111105
0.8402777775 + -1.833333333x + x2 = 2.1736111105

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = 2.1736111105

Calculate the square root of the right side: 1.474317168

Break this problem into two subproblems by setting 
(x + -0.9166666665) equal to 1.474317168 and -1.474317168.

Subproblem 1

x + -0.9166666665 = 1.474317168 Simplifying x + -0.9166666665 = 1.474317168 Reorder the terms: -0.9166666665 + x = 1.474317168 Solving -0.9166666665 + x = 1.474317168 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 = 1.474317168 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.474317168 + 0.9166666665 x = 1.474317168 + 0.9166666665 Combine like terms: 1.474317168 + 0.9166666665 = 2.3909838345 x = 2.3909838345 Simplifying x = 2.3909838345

Subproblem 2

x + -0.9166666665 = -1.474317168 Simplifying x + -0.9166666665 = -1.474317168 Reorder the terms: -0.9166666665 + x = -1.474317168 Solving -0.9166666665 + x = -1.474317168 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 = -1.474317168 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.474317168 + 0.9166666665 x = -1.474317168 + 0.9166666665 Combine like terms: -1.474317168 + 0.9166666665 = -0.5576505015 x = -0.5576505015 Simplifying x = -0.5576505015

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.3909838345, -0.5576505015}

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