6x^2-11x-5=0

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Solution for 6x^2-11x-5=0 equation: 


Simplifying
6x2 + -11x + -5 = 0

Reorder the terms:
-5 + -11x + 6x2 = 0

Solving
-5 + -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'.
-0.8333333333 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -1.833333333x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -1.833333333x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -1.833333333x + x2 = 0 + 0.8333333333
-1.833333333x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-1.833333333x + x2 = 0.8333333333

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 = 0.8333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = 0.8333333333 + 0.8402777775

Combine like terms: 0.8333333333 + 0.8402777775 = 1.6736111108
0.8402777775 + -1.833333333x + x2 = 1.6736111108

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = 1.6736111108

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + -0.9166666665) equal to 1.293681225 and -1.293681225.


Subproblem 1
x + -0.9166666665 = 1.293681225

Simplifying
x + -0.9166666665 = 1.293681225

Reorder the terms:
-0.9166666665 + x = 1.293681225

Solving
-0.9166666665 + x = 1.293681225

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 = 1.293681225 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = 1.293681225 + 0.9166666665
x = 1.293681225 + 0.9166666665

Combine like terms: 1.293681225 + 0.9166666665 = 2.2103478915
x = 2.2103478915

Simplifying
x = 2.2103478915


Subproblem 2
x + -0.9166666665 = -1.293681225

Simplifying
x + -0.9166666665 = -1.293681225

Reorder the terms:
-0.9166666665 + x = -1.293681225

Solving
-0.9166666665 + x = -1.293681225

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 = -1.293681225 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = -1.293681225 + 0.9166666665
x = -1.293681225 + 0.9166666665

Combine like terms: -1.293681225 + 0.9166666665 = -0.3770145585
x = -0.3770145585

Simplifying
x = -0.3770145585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2103478915, -0.3770145585}

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