-3x^2+x=-11

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

Simplifying
-3x2 + x = -11

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

Solving
x + -3x2 = -11

Solving for variable 'x'.

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

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

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-3.666666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -0.3333333333x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -0.3333333333x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -0.3333333333x + x2 = 0 + 3.666666667
-0.3333333333x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-0.3333333333x + x2 = 3.666666667

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.
-0.3333333333x + 0.25 + x2 = 3.666666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333x + x2 = 3.666666667 + 0.25

Combine like terms: 3.666666667 + 0.25 = 3.916666667
0.25 + -0.3333333333x + x2 = 3.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.979057015 and -1.979057015.

Subproblem 1
x + 0.5 = 1.979057015

Simplifying
x + 0.5 = 1.979057015

Reorder the terms:
0.5 + x = 1.979057015

Solving
0.5 + x = 1.979057015

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.979057015 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.979057015 + -0.5
x = 1.979057015 + -0.5

Combine like terms: 1.979057015 + -0.5 = 1.479057015
x = 1.479057015

Simplifying
x = 1.479057015

Subproblem 2
x + 0.5 = -1.979057015

Simplifying
x + 0.5 = -1.979057015

Reorder the terms:
0.5 + x = -1.979057015

Solving
0.5 + x = -1.979057015

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.979057015 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.979057015 + -0.5
x = -1.979057015 + -0.5

Combine like terms: -1.979057015 + -0.5 = -2.479057015
x = -2.479057015

Simplifying
x = -2.479057015

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.479057015, -2.479057015}