(x-5)(x-5)=16

Solution for (x-5)(x-5)=16 equation:

Simplifying
(x + -5)(x + -5) = 16

Reorder the terms:
(-5 + x)(x + -5) = 16

Reorder the terms:
(-5 + x)(-5 + x) = 16

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) = 16
((-5 * -5 + x * -5) + x(-5 + x)) = 16
((25 + -5x) + x(-5 + x)) = 16
(25 + -5x + (-5 * x + x * x)) = 16
(25 + -5x + (-5x + x2)) = 16

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) = 16

Solving
25 + -10x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
25 + -16 + -10x + x2 = 16 + -16

Combine like terms: 25 + -16 = 9
9 + -10x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
9 + -10x + x2 = 0

Factor a trinomial.
(1 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {1, 9}