(x-9)(x-9)=1

Solution for (x-9)(x-9)=1 equation:

Simplifying
(x + -9)(x + -9) = 1

Reorder the terms:
(-9 + x)(x + -9) = 1

Reorder the terms:
(-9 + x)(-9 + x) = 1

Multiply (-9 + x) * (-9 + x)
(-9(-9 + x) + x(-9 + x)) = 1
((-9 * -9 + x * -9) + x(-9 + x)) = 1
((81 + -9x) + x(-9 + x)) = 1
(81 + -9x + (-9 * x + x * x)) = 1
(81 + -9x + (-9x + x2)) = 1

Combine like terms: -9x + -9x = -18x
(81 + -18x + x2) = 1

Solving
81 + -18x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
81 + -1 + -18x + x2 = 1 + -1

Combine like terms: 81 + -1 = 80
80 + -18x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
80 + -18x + x2 = 0

Factor a trinomial.
(8 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {8, 10}