6x^2+11x-6=0

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


Simplifying
6x2 + 11x + -6 = 0

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

Solving
-6 + 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 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.833333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.833333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.833333333x + x2 = 0 + 1
1.833333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.833333333x + x2 = 1

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 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 1 + 0.8402777775

Combine like terms: 1 + 0.8402777775 = 1.8402777775
0.8402777775 + 1.833333333x + x2 = 1.8402777775

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 1.8402777775

Calculate the square root of the right side: 1.356568383

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 1.356568383 and -1.356568383.

Subproblem 1

x + 0.9166666665 = 1.356568383 Simplifying x + 0.9166666665 = 1.356568383 Reorder the terms: 0.9166666665 + x = 1.356568383 Solving 0.9166666665 + x = 1.356568383 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 = 1.356568383 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.356568383 + -0.9166666665 x = 1.356568383 + -0.9166666665 Combine like terms: 1.356568383 + -0.9166666665 = 0.4399017165 x = 0.4399017165 Simplifying x = 0.4399017165

Subproblem 2

x + 0.9166666665 = -1.356568383 Simplifying x + 0.9166666665 = -1.356568383 Reorder the terms: 0.9166666665 + x = -1.356568383 Solving 0.9166666665 + x = -1.356568383 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 = -1.356568383 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.356568383 + -0.9166666665 x = -1.356568383 + -0.9166666665 Combine like terms: -1.356568383 + -0.9166666665 = -2.2732350495 x = -2.2732350495 Simplifying x = -2.2732350495

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4399017165, -2.2732350495}

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