-11x^2=x+11

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

Simplifying
-11x2 = x + 11

Reorder the terms:
-11x2 = 11 + x

Solving
-11x2 = 11 + x

Solving for variable 'x'.

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

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

Combine like terms: 11 + -11 = 0
-11 + -1x + -11x2 = 0 + x + -1x
-11 + -1x + -11x2 = x + -1x

Combine like terms: x + -1x = 0
-11 + -1x + -11x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + x + 11x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + x + 11x2)' equal to zero and attempt to solve:

Simplifying
11 + x + 11x2 = 0

Solving
11 + x + 11x2 = 0

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

Divide each side by '11'.
1 + 0.09090909091x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.09090909091x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 0.09090909091x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.09090909091x + x2 = 0 + -1
0.09090909091x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.09090909091x + x2 = -1

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.09090909091x + 0.25 + x2 = -1 + 0.25

Reorder the terms:
0.25 + 0.09090909091x + x2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.09090909091x + x2 = -0.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.