(x-10)(x-10)=121

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Solution for (x-10)(x-10)=121 equation: 


Simplifying
(x + -10)(x + -10) = 121

Reorder the terms:
(-10 + x)(x + -10) = 121

Reorder the terms:
(-10 + x)(-10 + x) = 121

Multiply (-10 + x) * (-10 + x)
(-10(-10 + x) + x(-10 + x)) = 121
((-10 * -10 + x * -10) + x(-10 + x)) = 121
((100 + -10x) + x(-10 + x)) = 121
(100 + -10x + (-10 * x + x * x)) = 121
(100 + -10x + (-10x + x2)) = 121

Combine like terms: -10x + -10x = -20x
(100 + -20x + x2) = 121

Solving
100 + -20x + x2 = 121

Solving for variable 'x'.

Reorder the terms:
100 + -121 + -20x + x2 = 121 + -121

Combine like terms: 100 + -121 = -21
-21 + -20x + x2 = 121 + -121

Combine like terms: 121 + -121 = 0
-21 + -20x + x2 = 0

Factor a trinomial.
(-1 + -1x)(21 + -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 '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {-1, 21}

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