11x^2+12x-6=0

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Solution for 11x^2+12x-6=0 equation:


Simplifying
11x2 + 12x + -6 = 0

Reorder the terms:
-6 + 12x + 11x2 = 0

Solving
-6 + 12x + 11x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
11 the coefficient of the squared term: 

Divide each side by '11'.
-0.5454545455 + 1.090909091x + x2 = 0

Move the constant term to the right:

Add '0.5454545455' to each side of the equation.
-0.5454545455 + 1.090909091x + 0.5454545455 + x2 = 0 + 0.5454545455

Reorder the terms:
-0.5454545455 + 0.5454545455 + 1.090909091x + x2 = 0 + 0.5454545455

Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000
0.0000000000 + 1.090909091x + x2 = 0 + 0.5454545455
1.090909091x + x2 = 0 + 0.5454545455

Combine like terms: 0 + 0.5454545455 = 0.5454545455
1.090909091x + x2 = 0.5454545455

The x term is 1.090909091x.  Take half its coefficient (0.5454545455).
Square it (0.2975206612) and add it to both sides.

Add '0.2975206612' to each side of the equation.
1.090909091x + 0.2975206612 + x2 = 0.5454545455 + 0.2975206612

Reorder the terms:
0.2975206612 + 1.090909091x + x2 = 0.5454545455 + 0.2975206612

Combine like terms: 0.5454545455 + 0.2975206612 = 0.8429752067
0.2975206612 + 1.090909091x + x2 = 0.8429752067

Factor a perfect square on the left side:
(x + 0.5454545455)(x + 0.5454545455) = 0.8429752067

Calculate the square root of the right side: 0.918136813

Break this problem into two subproblems by setting 
(x + 0.5454545455) equal to 0.918136813 and -0.918136813.

Subproblem 1

x + 0.5454545455 = 0.918136813 Simplifying x + 0.5454545455 = 0.918136813 Reorder the terms: 0.5454545455 + x = 0.918136813 Solving 0.5454545455 + x = 0.918136813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + x = 0.918136813 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = 0.918136813 + -0.5454545455 x = 0.918136813 + -0.5454545455 Combine like terms: 0.918136813 + -0.5454545455 = 0.3726822675 x = 0.3726822675 Simplifying x = 0.3726822675

Subproblem 2

x + 0.5454545455 = -0.918136813 Simplifying x + 0.5454545455 = -0.918136813 Reorder the terms: 0.5454545455 + x = -0.918136813 Solving 0.5454545455 + x = -0.918136813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + x = -0.918136813 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = -0.918136813 + -0.5454545455 x = -0.918136813 + -0.5454545455 Combine like terms: -0.918136813 + -0.5454545455 = -1.4635913585 x = -1.4635913585 Simplifying x = -1.4635913585

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3726822675, -1.4635913585}

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