(x-11)(x-11)=144

Solution for (x-11)(x-11)=144 equation:

Simplifying
(x + -11)(x + -11) = 144

Reorder the terms:
(-11 + x)(x + -11) = 144

Reorder the terms:
(-11 + x)(-11 + x) = 144

Multiply (-11 + x) * (-11 + x)
(-11(-11 + x) + x(-11 + x)) = 144
((-11 * -11 + x * -11) + x(-11 + x)) = 144
((121 + -11x) + x(-11 + x)) = 144
(121 + -11x + (-11 * x + x * x)) = 144
(121 + -11x + (-11x + x2)) = 144

Combine like terms: -11x + -11x = -22x
(121 + -22x + x2) = 144

Solving
121 + -22x + x2 = 144

Solving for variable 'x'.

Reorder the terms:
121 + -144 + -22x + x2 = 144 + -144

Combine like terms: 121 + -144 = -23
-23 + -22x + x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-23 + -22x + x2 = 0

Factor a trinomial.
(-1 + -1x)(23 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(23 + -1x)' equal to zero and attempt to solve:

Simplifying
23 + -1x = 0

Solving
23 + -1x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1x = 0 + -23
-1x = 0 + -23

Combine like terms: 0 + -23 = -23
-1x = -23

Divide each side by '-1'.
x = 23

Simplifying
x = 23
Solution
x = {-1, 23}