(x-5)(x-5)-100=0

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Solution for (x-5)(x-5)-100=0 equation: 


Simplifying
(x + -5)(x + -5) + -100 = 0

Reorder the terms:
(-5 + x)(x + -5) + -100 = 0

Reorder the terms:
(-5 + x)(-5 + x) + -100 = 0

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + -100 = 0
((-5 * -5 + x * -5) + x(-5 + x)) + -100 = 0
((25 + -5x) + x(-5 + x)) + -100 = 0
(25 + -5x + (-5 * x + x * x)) + -100 = 0
(25 + -5x + (-5x + x2)) + -100 = 0

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + -100 = 0

Reorder the terms:
25 + -100 + -10x + x2 = 0

Combine like terms: 25 + -100 = -75
-75 + -10x + x2 = 0

Solving
-75 + -10x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(15 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-5, 15}

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