11x^2-x-1=0

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Solution for 11x^2-x-1=0 equation:


Simplifying
11x2 + -1x + -1 = 0

Reorder the terms:
-1 + -1x + 11x2 = 0

Solving
-1 + -1x + 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 + -0.09090909091x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -0.09090909091x.  Take half its coefficient (-0.04545454546).
Square it (0.002066115703) and add it to both sides.

Add '0.002066115703' to each side of the equation.
-0.09090909091x + 0.002066115703 + x2 = 0.09090909091 + 0.002066115703

Reorder the terms:
0.002066115703 + -0.09090909091x + x2 = 0.09090909091 + 0.002066115703

Combine like terms: 0.09090909091 + 0.002066115703 = 0.092975206613
0.002066115703 + -0.09090909091x + x2 = 0.092975206613

Factor a perfect square on the left side:
(x + -0.04545454546)(x + -0.04545454546) = 0.092975206613

Calculate the square root of the right side: 0.304918361

Break this problem into two subproblems by setting 
(x + -0.04545454546) equal to 0.304918361 and -0.304918361.

Subproblem 1

x + -0.04545454546 = 0.304918361 Simplifying x + -0.04545454546 = 0.304918361 Reorder the terms: -0.04545454546 + x = 0.304918361 Solving -0.04545454546 + x = 0.304918361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x = 0.304918361 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = 0.304918361 + 0.04545454546 x = 0.304918361 + 0.04545454546 Combine like terms: 0.304918361 + 0.04545454546 = 0.35037290646 x = 0.35037290646 Simplifying x = 0.35037290646

Subproblem 2

x + -0.04545454546 = -0.304918361 Simplifying x + -0.04545454546 = -0.304918361 Reorder the terms: -0.04545454546 + x = -0.304918361 Solving -0.04545454546 + x = -0.304918361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x = -0.304918361 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = -0.304918361 + 0.04545454546 x = -0.304918361 + 0.04545454546 Combine like terms: -0.304918361 + 0.04545454546 = -0.25946381554 x = -0.25946381554 Simplifying x = -0.25946381554

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.35037290646, -0.25946381554}

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