2(x+6)=x^2

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

Simplifying
2(x + 6) = x2

Reorder the terms:
2(6 + x) = x2
(6 * 2 + x * 2) = x2
(12 + 2x) = x2

Solving
12 + 2x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
12 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-12 + -2x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -2x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -2x + x2 = 0 + 12

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

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

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 12 + 1

Reorder the terms:
1 + -2x + x2 = 12 + 1

Combine like terms: 12 + 1 = 13
1 + -2x + x2 = 13

Factor a perfect square on the left side:
(x + -1)(x + -1) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -1) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + -1 = 3.605551275

Simplifying
x + -1 = 3.605551275

Reorder the terms:
-1 + x = 3.605551275

Solving
-1 + x = 3.605551275

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.605551275 + 1
x = 3.605551275 + 1

Combine like terms: 3.605551275 + 1 = 4.605551275
x = 4.605551275

Simplifying
x = 4.605551275

Subproblem 2
x + -1 = -3.605551275

Simplifying
x + -1 = -3.605551275

Reorder the terms:
-1 + x = -3.605551275

Solving
-1 + x = -3.605551275

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.605551275 + 1
x = -3.605551275 + 1

Combine like terms: -3.605551275 + 1 = -2.605551275
x = -2.605551275

Simplifying
x = -2.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.605551275, -2.605551275}