x+16=x(x+12)

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Solution for x+16=x(x+12) equation: 


Simplifying
x + 16 = x(x + 12)

Reorder the terms:
16 + x = x(x + 12)

Reorder the terms:
16 + x = x(12 + x)
16 + x = (12 * x + x * x)
16 + x = (12x + x2)

Solving
16 + x = 12x + x2

Solving for variable 'x'.

Combine like terms: x + -12x = -11x
16 + -11x + -1x2 = 12x + x2 + -12x + -1x2

Reorder the terms:
16 + -11x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
16 + -11x + -1x2 = 0 + x2 + -1x2
16 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + 11x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 11x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 11x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 11x + x2 = 0 + 16
11x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
11x + x2 = 16

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 = 16 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 16 + 30.25

Combine like terms: 16 + 30.25 = 46.25
30.25 + 11x + x2 = 46.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(x + 5.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
x + 5.5 = 6.800735254

Simplifying
x + 5.5 = 6.800735254

Reorder the terms:
5.5 + x = 6.800735254

Solving
5.5 + x = 6.800735254

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 = 6.800735254 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 6.800735254 + -5.5
x = 6.800735254 + -5.5

Combine like terms: 6.800735254 + -5.5 = 1.300735254
x = 1.300735254

Simplifying
x = 1.300735254


Subproblem 2
x + 5.5 = -6.800735254

Simplifying
x + 5.5 = -6.800735254

Reorder the terms:
5.5 + x = -6.800735254

Solving
5.5 + x = -6.800735254

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 = -6.800735254 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -6.800735254 + -5.5
x = -6.800735254 + -5.5

Combine like terms: -6.800735254 + -5.5 = -12.300735254
x = -12.300735254

Simplifying
x = -12.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.300735254, -12.300735254}

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