(x-9)(x-9)-25=0

Solution for (x-9)(x-9)-25=0 equation:

Simplifying
(x + -9)(x + -9) + -25 = 0

Reorder the terms:
(-9 + x)(x + -9) + -25 = 0

Reorder the terms:
(-9 + x)(-9 + x) + -25 = 0

Multiply (-9 + x) * (-9 + x)
(-9(-9 + x) + x(-9 + x)) + -25 = 0
((-9 * -9 + x * -9) + x(-9 + x)) + -25 = 0
((81 + -9x) + x(-9 + x)) + -25 = 0
(81 + -9x + (-9 * x + x * x)) + -25 = 0
(81 + -9x + (-9x + x2)) + -25 = 0

Combine like terms: -9x + -9x = -18x
(81 + -18x + x2) + -25 = 0

Reorder the terms:
81 + -25 + -18x + x2 = 0

Combine like terms: 81 + -25 = 56
56 + -18x + x2 = 0

Solving
56 + -18x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(14 + -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 '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {4, 14}