7(x+6)=x^2

Solution for 7(x+6)=x^2 equation:

Simplifying
7(x + 6) = x2

Reorder the terms:
7(6 + x) = x2
(6 * 7 + x * 7) = x2
(42 + 7x) = x2

Solving
42 + 7x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
42 + 7x + -1x2 = 0

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

Divide each side by '-1'.
-42 + -7x + x2 = 0

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -7x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + -7x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -7x + x2 = 0 + 42
-7x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
-7x + x2 = 42

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 42 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 42 + 12.25

Combine like terms: 42 + 12.25 = 54.25
12.25 + -7x + x2 = 54.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + -3.5) equal to 7.365459931 and -7.365459931.

Subproblem 1
x + -3.5 = 7.365459931

Simplifying
x + -3.5 = 7.365459931

Reorder the terms:
-3.5 + x = 7.365459931

Solving
-3.5 + x = 7.365459931

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 7.365459931 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 7.365459931 + 3.5
x = 7.365459931 + 3.5

Combine like terms: 7.365459931 + 3.5 = 10.865459931
x = 10.865459931

Simplifying
x = 10.865459931

Subproblem 2
x + -3.5 = -7.365459931

Simplifying
x + -3.5 = -7.365459931

Reorder the terms:
-3.5 + x = -7.365459931

Solving
-3.5 + x = -7.365459931

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -7.365459931 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -7.365459931 + 3.5
x = -7.365459931 + 3.5

Combine like terms: -7.365459931 + 3.5 = -3.865459931
x = -3.865459931

Simplifying
x = -3.865459931

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.865459931, -3.865459931}