(x-5)(x-5)+1=26

Solution for (x-5)(x-5)+1=26 equation:

Simplifying
(x + -5)(x + -5) + 1 = 26

Reorder the terms:
(-5 + x)(x + -5) + 1 = 26

Reorder the terms:
(-5 + x)(-5 + x) + 1 = 26

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + 1 = 26
((-5 * -5 + x * -5) + x(-5 + x)) + 1 = 26
((25 + -5x) + x(-5 + x)) + 1 = 26
(25 + -5x + (-5 * x + x * x)) + 1 = 26
(25 + -5x + (-5x + x2)) + 1 = 26

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + 1 = 26

Reorder the terms:
25 + 1 + -10x + x2 = 26

Combine like terms: 25 + 1 = 26
26 + -10x + x2 = 26

Add '-26' to each side of the equation.
26 + -10x + -26 + x2 = 26 + -26

Reorder the terms:
26 + -26 + -10x + x2 = 26 + -26

Combine like terms: 26 + -26 = 0
0 + -10x + x2 = 26 + -26
-10x + x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-10x + x2 = 0

Solving
-10x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 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 + x = 0 + 10

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

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

Simplifying
x = 10
Solution
x = {0, 10}