x^2+4x+x^2+8x+x^2+4x+8x+16=262

Solution for x^2+4x+x^2+8x+x^2+4x+8x+16=262 equation:

Simplifying
x2 + 4x + x2 + 8x + x2 + 4x + 8x + 16 = 262

Reorder the terms:
16 + 4x + 8x + 4x + 8x + x2 + x2 + x2 = 262

Combine like terms: 4x + 8x = 12x
16 + 12x + 4x + 8x + x2 + x2 + x2 = 262

Combine like terms: 12x + 4x = 16x
16 + 16x + 8x + x2 + x2 + x2 = 262

Combine like terms: 16x + 8x = 24x
16 + 24x + x2 + x2 + x2 = 262

Combine like terms: x2 + x2 = 2x2
16 + 24x + 2x2 + x2 = 262

Combine like terms: 2x2 + x2 = 3x2
16 + 24x + 3x2 = 262

Solving
16 + 24x + 3x2 = 262

Solving for variable 'x'.

Reorder the terms:
16 + -262 + 24x + 3x2 = 262 + -262

Combine like terms: 16 + -262 = -246
-246 + 24x + 3x2 = 262 + -262

Combine like terms: 262 + -262 = 0
-246 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-82 + 8x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-82 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-82 + 8x + x2 = 0

Solving
-82 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '82' to each side of the equation.
-82 + 8x + 82 + x2 = 0 + 82

Reorder the terms:
-82 + 82 + 8x + x2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + 8x + x2 = 0 + 82
8x + x2 = 0 + 82

Combine like terms: 0 + 82 = 82
8x + x2 = 82

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 82 + 16

Reorder the terms:
16 + 8x + x2 = 82 + 16

Combine like terms: 82 + 16 = 98
16 + 8x + x2 = 98

Factor a perfect square on the left side:
(x + 4)(x + 4) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + 4) equal to 9.899494937 and -9.899494937.

Subproblem 1
x + 4 = 9.899494937

Simplifying
x + 4 = 9.899494937

Reorder the terms:
4 + x = 9.899494937

Solving
4 + x = 9.899494937

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 9.899494937 + -4

Combine like terms: 4 + -4 = 0
0 + x = 9.899494937 + -4
x = 9.899494937 + -4

Combine like terms: 9.899494937 + -4 = 5.899494937
x = 5.899494937

Simplifying
x = 5.899494937

Subproblem 2
x + 4 = -9.899494937

Simplifying
x + 4 = -9.899494937

Reorder the terms:
4 + x = -9.899494937

Solving
4 + x = -9.899494937

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -9.899494937 + -4

Combine like terms: 4 + -4 = 0
0 + x = -9.899494937 + -4
x = -9.899494937 + -4

Combine like terms: -9.899494937 + -4 = -13.899494937
x = -13.899494937

Simplifying
x = -13.899494937

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.899494937, -13.899494937}
Solution
x = {5.899494937, -13.899494937}