66=(x+3)(x+3)

Solution for 66=(x+3)(x+3) equation:

Simplifying
66 = (x + 3)(x + 3)

Reorder the terms:
66 = (3 + x)(x + 3)

Reorder the terms:
66 = (3 + x)(3 + x)

Multiply (3 + x) * (3 + x)
66 = (3(3 + x) + x(3 + x))
66 = ((3 * 3 + x * 3) + x(3 + x))
66 = ((9 + 3x) + x(3 + x))
66 = (9 + 3x + (3 * x + x * x))
66 = (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
66 = (9 + 6x + x2)

Solving
66 = 9 + 6x + x2

Solving for variable 'x'.

Combine like terms: 66 + -9 = 57
57 + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
57 + -6x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
57 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2
57 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
57 + -6x + -1x2 = 0 + x2 + -1x2
57 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
57 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-57 + 6x + x2 = 0

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + 6x + 57 + x2 = 0 + 57

Reorder the terms:
-57 + 57 + 6x + x2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + 6x + x2 = 0 + 57
6x + x2 = 0 + 57

Combine like terms: 0 + 57 = 57
6x + x2 = 57

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 57 + 9

Reorder the terms:
9 + 6x + x2 = 57 + 9

Combine like terms: 57 + 9 = 66
9 + 6x + x2 = 66

Factor a perfect square on the left side:
(x + 3)(x + 3) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(x + 3) equal to 8.124038405 and -8.124038405.

Subproblem 1
x + 3 = 8.124038405

Simplifying
x + 3 = 8.124038405

Reorder the terms:
3 + x = 8.124038405

Solving
3 + x = 8.124038405

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 8.124038405 + -3

Combine like terms: 3 + -3 = 0
0 + x = 8.124038405 + -3
x = 8.124038405 + -3

Combine like terms: 8.124038405 + -3 = 5.124038405
x = 5.124038405

Simplifying
x = 5.124038405

Subproblem 2
x + 3 = -8.124038405

Simplifying
x + 3 = -8.124038405

Reorder the terms:
3 + x = -8.124038405

Solving
3 + x = -8.124038405

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -8.124038405 + -3

Combine like terms: 3 + -3 = 0
0 + x = -8.124038405 + -3
x = -8.124038405 + -3

Combine like terms: -8.124038405 + -3 = -11.124038405
x = -11.124038405

Simplifying
x = -11.124038405

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.124038405, -11.124038405}