(x+11)(x+11)=256

Solution for (x+11)(x+11)=256 equation:

Simplifying
(x + 11)(x + 11) = 256

Reorder the terms:
(11 + x)(x + 11) = 256

Reorder the terms:
(11 + x)(11 + x) = 256

Multiply (11 + x) * (11 + x)
(11(11 + x) + x(11 + x)) = 256
((11 * 11 + x * 11) + x(11 + x)) = 256
((121 + 11x) + x(11 + x)) = 256
(121 + 11x + (11 * x + x * x)) = 256
(121 + 11x + (11x + x2)) = 256

Combine like terms: 11x + 11x = 22x
(121 + 22x + x2) = 256

Solving
121 + 22x + x2 = 256

Solving for variable 'x'.

Reorder the terms:
121 + -256 + 22x + x2 = 256 + -256

Combine like terms: 121 + -256 = -135
-135 + 22x + x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-135 + 22x + x2 = 0

Factor a trinomial.
(-27 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-27 + -1x)' equal to zero and attempt to solve:

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

Simplifying
x = -27
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-27, 5}