x^2+(x+6)(x+6)=481

Solution for x^2+(x+6)(x+6)=481 equation:

Simplifying
x2 + (x + 6)(x + 6) = 481

Reorder the terms:
x2 + (6 + x)(x + 6) = 481

Reorder the terms:
x2 + (6 + x)(6 + x) = 481

Multiply (6 + x) * (6 + x)
x2 + (6(6 + x) + x(6 + x)) = 481
x2 + ((6 * 6 + x * 6) + x(6 + x)) = 481
x2 + ((36 + 6x) + x(6 + x)) = 481
x2 + (36 + 6x + (6 * x + x * x)) = 481
x2 + (36 + 6x + (6x + x2)) = 481

Combine like terms: 6x + 6x = 12x
x2 + (36 + 12x + x2) = 481

Reorder the terms:
36 + 12x + x2 + x2 = 481

Combine like terms: x2 + x2 = 2x2
36 + 12x + 2x2 = 481

Solving
36 + 12x + 2x2 = 481

Solving for variable 'x'.

Reorder the terms:
36 + -481 + 12x + 2x2 = 481 + -481

Combine like terms: 36 + -481 = -445
-445 + 12x + 2x2 = 481 + -481

Combine like terms: 481 + -481 = 0
-445 + 12x + 2x2 = 0

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

Divide each side by '2'.
-222.5 + 6x + x2 = 0

Move the constant term to the right:

Add '222.5' to each side of the equation.
-222.5 + 6x + 222.5 + x2 = 0 + 222.5

Reorder the terms:
-222.5 + 222.5 + 6x + x2 = 0 + 222.5

Combine like terms: -222.5 + 222.5 = 0.0
0.0 + 6x + x2 = 0 + 222.5
6x + x2 = 0 + 222.5

Combine like terms: 0 + 222.5 = 222.5
6x + x2 = 222.5

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 = 222.5 + 9

Reorder the terms:
9 + 6x + x2 = 222.5 + 9

Combine like terms: 222.5 + 9 = 231.5
9 + 6x + x2 = 231.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 231.5

Calculate the square root of the right side: 15.215124055

Break this problem into two subproblems by setting 
(x + 3) equal to 15.215124055 and -15.215124055.

Subproblem 1
x + 3 = 15.215124055

Simplifying
x + 3 = 15.215124055

Reorder the terms:
3 + x = 15.215124055

Solving
3 + x = 15.215124055

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 = 15.215124055 + -3

Combine like terms: 3 + -3 = 0
0 + x = 15.215124055 + -3
x = 15.215124055 + -3

Combine like terms: 15.215124055 + -3 = 12.215124055
x = 12.215124055

Simplifying
x = 12.215124055

Subproblem 2
x + 3 = -15.215124055

Simplifying
x + 3 = -15.215124055

Reorder the terms:
3 + x = -15.215124055

Solving
3 + x = -15.215124055

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 = -15.215124055 + -3

Combine like terms: 3 + -3 = 0
0 + x = -15.215124055 + -3
x = -15.215124055 + -3

Combine like terms: -15.215124055 + -3 = -18.215124055
x = -18.215124055

Simplifying
x = -18.215124055

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.215124055, -18.215124055}