(X+6)(X+6)=33

Solution for (X+6)(X+6)=33 equation:

Simplifying
(X + 6)(X + 6) = 33

Reorder the terms:
(6 + X)(X + 6) = 33

Reorder the terms:
(6 + X)(6 + X) = 33

Multiply (6 + X) * (6 + X)
(6(6 + X) + X(6 + X)) = 33
((6 * 6 + X * 6) + X(6 + X)) = 33
((36 + 6X) + X(6 + X)) = 33
(36 + 6X + (6 * X + X * X)) = 33
(36 + 6X + (6X + X2)) = 33

Combine like terms: 6X + 6X = 12X
(36 + 12X + X2) = 33

Solving
36 + 12X + X2 = 33

Solving for variable 'X'.

Reorder the terms:
36 + -33 + 12X + X2 = 33 + -33

Combine like terms: 36 + -33 = 3
3 + 12X + X2 = 33 + -33

Combine like terms: 33 + -33 = 0
3 + 12X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 12X + -3 + X2 = 0 + -3

Reorder the terms:
3 + -3 + 12X + X2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 12X + X2 = 0 + -3
12X + X2 = 0 + -3

Combine like terms: 0 + -3 = -3
12X + X2 = -3

The X term is 12X.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12X + 36 + X2 = -3 + 36

Reorder the terms:
36 + 12X + X2 = -3 + 36

Combine like terms: -3 + 36 = 33
36 + 12X + X2 = 33

Factor a perfect square on the left side:
(X + 6)(X + 6) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(X + 6) equal to 5.744562647 and -5.744562647.

Subproblem 1
X + 6 = 5.744562647

Simplifying
X + 6 = 5.744562647

Reorder the terms:
6 + X = 5.744562647

Solving
6 + X = 5.744562647

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + -6 + X = 5.744562647 + -6

Combine like terms: 6 + -6 = 0
0 + X = 5.744562647 + -6
X = 5.744562647 + -6

Combine like terms: 5.744562647 + -6 = -0.255437353
X = -0.255437353

Simplifying
X = -0.255437353

Subproblem 2
X + 6 = -5.744562647

Simplifying
X + 6 = -5.744562647

Reorder the terms:
6 + X = -5.744562647

Solving
6 + X = -5.744562647

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + -6 + X = -5.744562647 + -6

Combine like terms: 6 + -6 = 0
0 + X = -5.744562647 + -6
X = -5.744562647 + -6

Combine like terms: -5.744562647 + -6 = -11.744562647
X = -11.744562647

Simplifying
X = -11.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.255437353, -11.744562647}