(x-2)(x-2)+9=25

Solution for (x-2)(x-2)+9=25 equation:

Simplifying
(x + -2)(x + -2) + 9 = 25

Reorder the terms:
(-2 + x)(x + -2) + 9 = 25

Reorder the terms:
(-2 + x)(-2 + x) + 9 = 25

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + 9 = 25
((-2 * -2 + x * -2) + x(-2 + x)) + 9 = 25
((4 + -2x) + x(-2 + x)) + 9 = 25
(4 + -2x + (-2 * x + x * x)) + 9 = 25
(4 + -2x + (-2x + x2)) + 9 = 25

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + 9 = 25

Reorder the terms:
4 + 9 + -4x + x2 = 25

Combine like terms: 4 + 9 = 13
13 + -4x + x2 = 25

Solving
13 + -4x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
13 + -25 + -4x + x2 = 25 + -25

Combine like terms: 13 + -25 = -12
-12 + -4x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-12 + -4x + x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 6}