11=4(x+1)x

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Solution for 11=4(x+1)x equation: 


Simplifying
11 = 4(x + 1) * x

Reorder the terms:
11 = 4(1 + x) * x

Reorder the terms for easier multiplication:
11 = 4x(1 + x)
11 = (1 * 4x + x * 4x)
11 = (4x + 4x2)

Solving
11 = 4x + 4x2

Solving for variable 'x'.

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

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

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

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.75 + x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x + x2 = 0 + 2.75
x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
x + x2 = 2.75

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.
 + 0.25 + x2 = 2.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 2.75 + 0.25

Combine like terms: 2.75 + 0.25 = 3
1.25 + x2 = 3

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + 0.5 = 1.732050808

Simplifying
x + 0.5 = 1.732050808

Reorder the terms:
0.5 + x = 1.732050808

Solving
0.5 + x = 1.732050808

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 = 1.732050808 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.732050808 + -0.5
x = 1.732050808 + -0.5

Combine like terms: 1.732050808 + -0.5 = 1.232050808
x = 1.232050808

Simplifying
x = 1.232050808


Subproblem 2
x + 0.5 = -1.732050808

Simplifying
x + 0.5 = -1.732050808

Reorder the terms:
0.5 + x = -1.732050808

Solving
0.5 + x = -1.732050808

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 = -1.732050808 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.732050808 + -0.5
x = -1.732050808 + -0.5

Combine like terms: -1.732050808 + -0.5 = -2.232050808
x = -2.232050808

Simplifying
x = -2.232050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.232050808, -2.232050808}

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