-(11x^2+6x-1)=

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Solution for -(11x^2+6x-1)= equation:


Simplifying
-1(11x2 + 6x + -1) = 0

Reorder the terms:
-1(-1 + 6x + 11x2) = 0
(-1 * -1 + 6x * -1 + 11x2 * -1) = 0
(1 + -6x + -11x2) = 0

Solving
1 + -6x + -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'.
-0.09090909091 + 0.5454545455x + x2 = 0

Move the constant term to the right:

Add '0.09090909091' to each side of the equation.
-0.09090909091 + 0.5454545455x + 0.09090909091 + x2 = 0 + 0.09090909091

Reorder the terms:
-0.09090909091 + 0.09090909091 + 0.5454545455x + x2 = 0 + 0.09090909091

Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000
0.00000000000 + 0.5454545455x + x2 = 0 + 0.09090909091
0.5454545455x + x2 = 0 + 0.09090909091

Combine like terms: 0 + 0.09090909091 = 0.09090909091
0.5454545455x + x2 = 0.09090909091

The x term is 0.5454545455x.  Take half its coefficient (0.2727272728).
Square it (0.07438016533) and add it to both sides.

Add '0.07438016533' to each side of the equation.
0.5454545455x + 0.07438016533 + x2 = 0.09090909091 + 0.07438016533

Reorder the terms:
0.07438016533 + 0.5454545455x + x2 = 0.09090909091 + 0.07438016533

Combine like terms: 0.09090909091 + 0.07438016533 = 0.16528925624
0.07438016533 + 0.5454545455x + x2 = 0.16528925624

Factor a perfect square on the left side:
(x + 0.2727272728)(x + 0.2727272728) = 0.16528925624

Calculate the square root of the right side: 0.406557814

Break this problem into two subproblems by setting 
(x + 0.2727272728) equal to 0.406557814 and -0.406557814.

Subproblem 1

x + 0.2727272728 = 0.406557814 Simplifying x + 0.2727272728 = 0.406557814 Reorder the terms: 0.2727272728 + x = 0.406557814 Solving 0.2727272728 + x = 0.406557814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = 0.406557814 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = 0.406557814 + -0.2727272728 x = 0.406557814 + -0.2727272728 Combine like terms: 0.406557814 + -0.2727272728 = 0.1338305412 x = 0.1338305412 Simplifying x = 0.1338305412

Subproblem 2

x + 0.2727272728 = -0.406557814 Simplifying x + 0.2727272728 = -0.406557814 Reorder the terms: 0.2727272728 + x = -0.406557814 Solving 0.2727272728 + x = -0.406557814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = -0.406557814 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = -0.406557814 + -0.2727272728 x = -0.406557814 + -0.2727272728 Combine like terms: -0.406557814 + -0.2727272728 = -0.6792850868 x = -0.6792850868 Simplifying x = -0.6792850868

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1338305412, -0.6792850868}

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