(x-9)(x-9)-2x=-19

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Solution for (x-9)(x-9)-2x=-19 equation: 


Simplifying
(x + -9)(x + -9) + -2x = -19

Reorder the terms:
(-9 + x)(x + -9) + -2x = -19

Reorder the terms:
(-9 + x)(-9 + x) + -2x = -19

Multiply (-9 + x) * (-9 + x)
(-9(-9 + x) + x(-9 + x)) + -2x = -19
((-9 * -9 + x * -9) + x(-9 + x)) + -2x = -19
((81 + -9x) + x(-9 + x)) + -2x = -19
(81 + -9x + (-9 * x + x * x)) + -2x = -19
(81 + -9x + (-9x + x2)) + -2x = -19

Combine like terms: -9x + -9x = -18x
(81 + -18x + x2) + -2x = -19

Reorder the terms:
81 + -18x + -2x + x2 = -19

Combine like terms: -18x + -2x = -20x
81 + -20x + x2 = -19

Solving
81 + -20x + x2 = -19

Solving for variable 'x'.

Reorder the terms:
81 + 19 + -20x + x2 = -19 + 19

Combine like terms: 81 + 19 = 100
100 + -20x + x2 = -19 + 19

Combine like terms: -19 + 19 = 0
100 + -20x + x2 = 0

Factor a trinomial.
(10 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {10, 10}

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