(x+2)(63+2x)=63

Solution for (x+2)(63+2x)=63 equation:

Simplifying
(x + 2)(63 + 2x) = 63

Reorder the terms:
(2 + x)(63 + 2x) = 63

Multiply (2 + x) * (63 + 2x)
(2(63 + 2x) + x(63 + 2x)) = 63
((63 * 2 + 2x * 2) + x(63 + 2x)) = 63
((126 + 4x) + x(63 + 2x)) = 63
(126 + 4x + (63 * x + 2x * x)) = 63
(126 + 4x + (63x + 2x2)) = 63

Combine like terms: 4x + 63x = 67x
(126 + 67x + 2x2) = 63

Solving
126 + 67x + 2x2 = 63

Solving for variable 'x'.

Reorder the terms:
126 + -63 + 67x + 2x2 = 63 + -63

Combine like terms: 126 + -63 = 63
63 + 67x + 2x2 = 63 + -63

Combine like terms: 63 + -63 = 0
63 + 67x + 2x2 = 0

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

Divide each side by '2'.
31.5 + 33.5x + x2 = 0

Move the constant term to the right:

Add '-31.5' to each side of the equation.
31.5 + 33.5x + -31.5 + x2 = 0 + -31.5

Reorder the terms:
31.5 + -31.5 + 33.5x + x2 = 0 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + 33.5x + x2 = 0 + -31.5
33.5x + x2 = 0 + -31.5

Combine like terms: 0 + -31.5 = -31.5
33.5x + x2 = -31.5

The x term is 33.5x.  Take half its coefficient (16.75).
Square it (280.5625) and add it to both sides.

Add '280.5625' to each side of the equation.
33.5x + 280.5625 + x2 = -31.5 + 280.5625

Reorder the terms:
280.5625 + 33.5x + x2 = -31.5 + 280.5625

Combine like terms: -31.5 + 280.5625 = 249.0625
280.5625 + 33.5x + x2 = 249.0625

Factor a perfect square on the left side:
(x + 16.75)(x + 16.75) = 249.0625

Calculate the square root of the right side: 15.781714102

Break this problem into two subproblems by setting 
(x + 16.75) equal to 15.781714102 and -15.781714102.

Subproblem 1
x + 16.75 = 15.781714102

Simplifying
x + 16.75 = 15.781714102

Reorder the terms:
16.75 + x = 15.781714102

Solving
16.75 + x = 15.781714102

Solving for variable 'x'.

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

Add '-16.75' to each side of the equation.
16.75 + -16.75 + x = 15.781714102 + -16.75

Combine like terms: 16.75 + -16.75 = 0.00
0.00 + x = 15.781714102 + -16.75
x = 15.781714102 + -16.75

Combine like terms: 15.781714102 + -16.75 = -0.968285898
x = -0.968285898

Simplifying
x = -0.968285898

Subproblem 2
x + 16.75 = -15.781714102

Simplifying
x + 16.75 = -15.781714102

Reorder the terms:
16.75 + x = -15.781714102

Solving
16.75 + x = -15.781714102

Solving for variable 'x'.

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

Add '-16.75' to each side of the equation.
16.75 + -16.75 + x = -15.781714102 + -16.75

Combine like terms: 16.75 + -16.75 = 0.00
0.00 + x = -15.781714102 + -16.75
x = -15.781714102 + -16.75

Combine like terms: -15.781714102 + -16.75 = -32.531714102
x = -32.531714102

Simplifying
x = -32.531714102

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.968285898, -32.531714102}