(x+64)(x-222)=666

Solution for (x+64)(x-222)=666 equation:

Simplifying
(x + 64)(x + -222) = 666

Reorder the terms:
(64 + x)(x + -222) = 666

Reorder the terms:
(64 + x)(-222 + x) = 666

Multiply (64 + x) * (-222 + x)
(64(-222 + x) + x(-222 + x)) = 666
((-222 * 64 + x * 64) + x(-222 + x)) = 666
((-14208 + 64x) + x(-222 + x)) = 666
(-14208 + 64x + (-222 * x + x * x)) = 666
(-14208 + 64x + (-222x + x2)) = 666

Combine like terms: 64x + -222x = -158x
(-14208 + -158x + x2) = 666

Solving
-14208 + -158x + x2 = 666

Solving for variable 'x'.

Reorder the terms:
-14208 + -666 + -158x + x2 = 666 + -666

Combine like terms: -14208 + -666 = -14874
-14874 + -158x + x2 = 666 + -666

Combine like terms: 666 + -666 = 0
-14874 + -158x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14874' to each side of the equation.
-14874 + -158x + 14874 + x2 = 0 + 14874

Reorder the terms:
-14874 + 14874 + -158x + x2 = 0 + 14874

Combine like terms: -14874 + 14874 = 0
0 + -158x + x2 = 0 + 14874
-158x + x2 = 0 + 14874

Combine like terms: 0 + 14874 = 14874
-158x + x2 = 14874

The x term is -158x.  Take half its coefficient (-79).
Square it (6241) and add it to both sides.

Add '6241' to each side of the equation.
-158x + 6241 + x2 = 14874 + 6241

Reorder the terms:
6241 + -158x + x2 = 14874 + 6241

Combine like terms: 14874 + 6241 = 21115
6241 + -158x + x2 = 21115

Factor a perfect square on the left side:
(x + -79)(x + -79) = 21115

Calculate the square root of the right side: 145.31001342

Break this problem into two subproblems by setting 
(x + -79) equal to 145.31001342 and -145.31001342.

Subproblem 1
x + -79 = 145.31001342

Simplifying
x + -79 = 145.31001342

Reorder the terms:
-79 + x = 145.31001342

Solving
-79 + x = 145.31001342

Solving for variable 'x'.

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

Add '79' to each side of the equation.
-79 + 79 + x = 145.31001342 + 79

Combine like terms: -79 + 79 = 0
0 + x = 145.31001342 + 79
x = 145.31001342 + 79

Combine like terms: 145.31001342 + 79 = 224.31001342
x = 224.31001342

Simplifying
x = 224.31001342

Subproblem 2
x + -79 = -145.31001342

Simplifying
x + -79 = -145.31001342

Reorder the terms:
-79 + x = -145.31001342

Solving
-79 + x = -145.31001342

Solving for variable 'x'.

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

Add '79' to each side of the equation.
-79 + 79 + x = -145.31001342 + 79

Combine like terms: -79 + 79 = 0
0 + x = -145.31001342 + 79
x = -145.31001342 + 79

Combine like terms: -145.31001342 + 79 = -66.31001342
x = -66.31001342

Simplifying
x = -66.31001342

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {224.31001342, -66.31001342}