11x^2-3x+2=4x+1

Solution for 11x^2-3x+2=4x+1 equation:

Simplifying
11x2 + -3x + 2 = 4x + 1

Reorder the terms:
2 + -3x + 11x2 = 4x + 1

Reorder the terms:
2 + -3x + 11x2 = 1 + 4x

Solving
2 + -3x + 11x2 = 1 + 4x

Solving for variable 'x'.

Reorder the terms:
2 + -1 + -3x + -4x + 11x2 = 1 + 4x + -1 + -4x

Combine like terms: 2 + -1 = 1
1 + -3x + -4x + 11x2 = 1 + 4x + -1 + -4x

Combine like terms: -3x + -4x = -7x
1 + -7x + 11x2 = 1 + 4x + -1 + -4x

Reorder the terms:
1 + -7x + 11x2 = 1 + -1 + 4x + -4x

Combine like terms: 1 + -1 = 0
1 + -7x + 11x2 = 0 + 4x + -4x
1 + -7x + 11x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
1 + -7x + 11x2 = 0

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

Divide each side by '11'.
0.09090909091 + -0.6363636364x + x2 = 0

Move the constant term to the right:

Add '-0.09090909091' to each side of the equation.
0.09090909091 + -0.6363636364x + -0.09090909091 + x2 = 0 + -0.09090909091

Reorder the terms:
0.09090909091 + -0.09090909091 + -0.6363636364x + x2 = 0 + -0.09090909091

Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000
0.00000000000 + -0.6363636364x + x2 = 0 + -0.09090909091
-0.6363636364x + x2 = 0 + -0.09090909091

Combine like terms: 0 + -0.09090909091 = -0.09090909091
-0.6363636364x + x2 = -0.09090909091

The x term is -0.6363636364x.  Take half its coefficient (-0.3181818182).
Square it (0.1012396694) and add it to both sides.

Add '0.1012396694' to each side of the equation.
-0.6363636364x + 0.1012396694 + x2 = -0.09090909091 + 0.1012396694

Reorder the terms:
0.1012396694 + -0.6363636364x + x2 = -0.09090909091 + 0.1012396694

Combine like terms: -0.09090909091 + 0.1012396694 = 0.01033057849
0.1012396694 + -0.6363636364x + x2 = 0.01033057849

Factor a perfect square on the left side:
(x + -0.3181818182)(x + -0.3181818182) = 0.01033057849

Calculate the square root of the right side: 0.101639453

Break this problem into two subproblems by setting 
(x + -0.3181818182) equal to 0.101639453 and -0.101639453.

Subproblem 1
x + -0.3181818182 = 0.101639453

Simplifying
x + -0.3181818182 = 0.101639453

Reorder the terms:
-0.3181818182 + x = 0.101639453

Solving
-0.3181818182 + x = 0.101639453

Solving for variable 'x'.

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

Add '0.3181818182' to each side of the equation.
-0.3181818182 + 0.3181818182 + x = 0.101639453 + 0.3181818182

Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000
0.0000000000 + x = 0.101639453 + 0.3181818182
x = 0.101639453 + 0.3181818182

Combine like terms: 0.101639453 + 0.3181818182 = 0.4198212712
x = 0.4198212712

Simplifying
x = 0.4198212712

Subproblem 2
x + -0.3181818182 = -0.101639453

Simplifying
x + -0.3181818182 = -0.101639453

Reorder the terms:
-0.3181818182 + x = -0.101639453

Solving
-0.3181818182 + x = -0.101639453

Solving for variable 'x'.

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

Add '0.3181818182' to each side of the equation.
-0.3181818182 + 0.3181818182 + x = -0.101639453 + 0.3181818182

Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000
0.0000000000 + x = -0.101639453 + 0.3181818182
x = -0.101639453 + 0.3181818182

Combine like terms: -0.101639453 + 0.3181818182 = 0.2165423652
x = 0.2165423652

Simplifying
x = 0.2165423652

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4198212712, 0.2165423652}