16+(x-3)=(x+3)(x+3)

Solution for 16+(x-3)=(x+3)(x+3) equation:

Simplifying
16 + (x + -3) = (x + 3)(x + 3)

Reorder the terms:
16 + (-3 + x) = (x + 3)(x + 3)

Remove parenthesis around (-3 + x)
16 + -3 + x = (x + 3)(x + 3)

Combine like terms: 16 + -3 = 13
13 + x = (x + 3)(x + 3)

Reorder the terms:
13 + x = (3 + x)(x + 3)

Reorder the terms:
13 + x = (3 + x)(3 + x)

Multiply (3 + x) * (3 + x)
13 + x = (3(3 + x) + x(3 + x))
13 + x = ((3 * 3 + x * 3) + x(3 + x))
13 + x = ((9 + 3x) + x(3 + x))
13 + x = (9 + 3x + (3 * x + x * x))
13 + x = (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
13 + x = (9 + 6x + x2)

Solving
13 + x = 9 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
13 + -9 + x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 13 + -9 = 4
4 + x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: x + -6x = -5x
4 + -5x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
4 + -5x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
4 + -5x + -1x2 = 0 + 6x + -6x + x2 + -1x2
4 + -5x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
4 + -5x + -1x2 = 0 + x2 + -1x2
4 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-4 + 5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5x + x2 = 0 + 4
5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
5x + x2 = 4

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 4 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5x + x2 = 10.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + 2.5 = 3.201562119

Simplifying
x + 2.5 = 3.201562119

Reorder the terms:
2.5 + x = 3.201562119

Solving
2.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.201562119 + -2.5
x = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
x = 0.701562119

Simplifying
x = 0.701562119

Subproblem 2
x + 2.5 = -3.201562119

Simplifying
x + 2.5 = -3.201562119

Reorder the terms:
2.5 + x = -3.201562119

Solving
2.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.201562119 + -2.5
x = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
x = -5.701562119

Simplifying
x = -5.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.701562119, -5.701562119}