-11x=x^2+3

Solution for -11x=x^2+3 equation:

Simplifying
-11x = x2 + 3

Reorder the terms:
-11x = 3 + x2

Solving
-11x = 3 + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -11x + -1x2 = 3 + x2 + -3 + -1x2

Reorder the terms:
-3 + -11x + -1x2 = 3 + -3 + x2 + -1x2

Combine like terms: 3 + -3 = 0
-3 + -11x + -1x2 = 0 + x2 + -1x2
-3 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -11x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 11x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 11x + x2 = 0

Solving
3 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 11x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 11x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 11x + x2 = 0 + -3
11x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
11x + x2 = -3

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -3 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -3 + 30.25

Combine like terms: -3 + 30.25 = 27.25
30.25 + 11x + x2 = 27.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
x + 5.5 = 5.220153254

Simplifying
x + 5.5 = 5.220153254

Reorder the terms:
5.5 + x = 5.220153254

Solving
5.5 + x = 5.220153254

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 5.220153254 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 5.220153254 + -5.5
x = 5.220153254 + -5.5

Combine like terms: 5.220153254 + -5.5 = -0.279846746
x = -0.279846746

Simplifying
x = -0.279846746

Subproblem 2
x + 5.5 = -5.220153254

Simplifying
x + 5.5 = -5.220153254

Reorder the terms:
5.5 + x = -5.220153254

Solving
5.5 + x = -5.220153254

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -5.220153254 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -5.220153254 + -5.5
x = -5.220153254 + -5.5

Combine like terms: -5.220153254 + -5.5 = -10.720153254
x = -10.720153254

Simplifying
x = -10.720153254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.279846746, -10.720153254}
Solution
x = {-0.279846746, -10.720153254}