(x-5)(x-5)-1=0

Solution for (x-5)(x-5)-1=0 equation:

Simplifying
(x + -5)(x + -5) + -1 = 0

Reorder the terms:
(-5 + x)(x + -5) + -1 = 0

Reorder the terms:
(-5 + x)(-5 + x) + -1 = 0

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + -1 = 0
((-5 * -5 + x * -5) + x(-5 + x)) + -1 = 0
((25 + -5x) + x(-5 + x)) + -1 = 0
(25 + -5x + (-5 * x + x * x)) + -1 = 0
(25 + -5x + (-5x + x2)) + -1 = 0

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + -1 = 0

Reorder the terms:
25 + -1 + -10x + x2 = 0

Combine like terms: 25 + -1 = 24
24 + -10x + x2 = 0

Solving
24 + -10x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}