(x-5)(x-5)-81=0

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Solution for (x-5)(x-5)-81=0 equation: 


Simplifying
(x + -5)(x + -5) + -81 = 0

Reorder the terms:
(-5 + x)(x + -5) + -81 = 0

Reorder the terms:
(-5 + x)(-5 + x) + -81 = 0

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + -81 = 0
((-5 * -5 + x * -5) + x(-5 + x)) + -81 = 0
((25 + -5x) + x(-5 + x)) + -81 = 0
(25 + -5x + (-5 * x + x * x)) + -81 = 0
(25 + -5x + (-5x + x2)) + -81 = 0

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + -81 = 0

Reorder the terms:
25 + -81 + -10x + x2 = 0

Combine like terms: 25 + -81 = -56
-56 + -10x + x2 = 0

Solving
-56 + -10x + 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}

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