(x+666)(x+666)=666

Solution for (x+666)(x+666)=666 equation:

Simplifying
(x + 666)(x + 666) = 666

Reorder the terms:
(666 + x)(x + 666) = 666

Reorder the terms:
(666 + x)(666 + x) = 666

Multiply (666 + x) * (666 + x)
(666(666 + x) + x(666 + x)) = 666
((666 * 666 + x * 666) + x(666 + x)) = 666
((443556 + 666x) + x(666 + x)) = 666
(443556 + 666x + (666 * x + x * x)) = 666
(443556 + 666x + (666x + x2)) = 666

Combine like terms: 666x + 666x = 1332x
(443556 + 1332x + x2) = 666

Solving
443556 + 1332x + x2 = 666

Solving for variable 'x'.

Reorder the terms:
443556 + -666 + 1332x + x2 = 666 + -666

Combine like terms: 443556 + -666 = 442890
442890 + 1332x + x2 = 666 + -666

Combine like terms: 666 + -666 = 0
442890 + 1332x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-442890' to each side of the equation.
442890 + 1332x + -442890 + x2 = 0 + -442890

Reorder the terms:
442890 + -442890 + 1332x + x2 = 0 + -442890

Combine like terms: 442890 + -442890 = 0
0 + 1332x + x2 = 0 + -442890
1332x + x2 = 0 + -442890

Combine like terms: 0 + -442890 = -442890
1332x + x2 = -442890

The x term is 1332x.  Take half its coefficient (666).
Square it (443556) and add it to both sides.

Add '443556' to each side of the equation.
1332x + 443556 + x2 = -442890 + 443556

Reorder the terms:
443556 + 1332x + x2 = -442890 + 443556

Combine like terms: -442890 + 443556 = 666
443556 + 1332x + x2 = 666

Factor a perfect square on the left side:
(x + 666)(x + 666) = 666

Calculate the square root of the right side: 25.806975801

Break this problem into two subproblems by setting 
(x + 666) equal to 25.806975801 and -25.806975801.

Subproblem 1
x + 666 = 25.806975801

Simplifying
x + 666 = 25.806975801

Reorder the terms:
666 + x = 25.806975801

Solving
666 + x = 25.806975801

Solving for variable 'x'.

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

Add '-666' to each side of the equation.
666 + -666 + x = 25.806975801 + -666

Combine like terms: 666 + -666 = 0
0 + x = 25.806975801 + -666
x = 25.806975801 + -666

Combine like terms: 25.806975801 + -666 = -640.193024199
x = -640.193024199

Simplifying
x = -640.193024199

Subproblem 2
x + 666 = -25.806975801

Simplifying
x + 666 = -25.806975801

Reorder the terms:
666 + x = -25.806975801

Solving
666 + x = -25.806975801

Solving for variable 'x'.

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

Add '-666' to each side of the equation.
666 + -666 + x = -25.806975801 + -666

Combine like terms: 666 + -666 = 0
0 + x = -25.806975801 + -666
x = -25.806975801 + -666

Combine like terms: -25.806975801 + -666 = -691.806975801
x = -691.806975801

Simplifying
x = -691.806975801

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-640.193024199, -691.806975801}