11-x=(x-9)(x-9)

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Solution for 11-x=(x-9)(x-9) equation: 


Simplifying
11 + -1x = (x + -9)(x + -9)

Reorder the terms:
11 + -1x = (-9 + x)(x + -9)

Reorder the terms:
11 + -1x = (-9 + x)(-9 + x)

Multiply (-9 + x) * (-9 + x)
11 + -1x = (-9(-9 + x) + x(-9 + x))
11 + -1x = ((-9 * -9 + x * -9) + x(-9 + x))
11 + -1x = ((81 + -9x) + x(-9 + x))
11 + -1x = (81 + -9x + (-9 * x + x * x))
11 + -1x = (81 + -9x + (-9x + x2))

Combine like terms: -9x + -9x = -18x
11 + -1x = (81 + -18x + x2)

Solving
11 + -1x = 81 + -18x + x2

Solving for variable 'x'.

Reorder the terms:
11 + -81 + -1x + 18x + -1x2 = 81 + -18x + x2 + -81 + 18x + -1x2

Combine like terms: 11 + -81 = -70
-70 + -1x + 18x + -1x2 = 81 + -18x + x2 + -81 + 18x + -1x2

Combine like terms: -1x + 18x = 17x
-70 + 17x + -1x2 = 81 + -18x + x2 + -81 + 18x + -1x2

Reorder the terms:
-70 + 17x + -1x2 = 81 + -81 + -18x + 18x + x2 + -1x2

Combine like terms: 81 + -81 = 0
-70 + 17x + -1x2 = 0 + -18x + 18x + x2 + -1x2
-70 + 17x + -1x2 = -18x + 18x + x2 + -1x2

Combine like terms: -18x + 18x = 0
-70 + 17x + -1x2 = 0 + x2 + -1x2
-70 + 17x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-70 + 17x + -1x2 = 0

Factor a trinomial.
(-10 + x)(7 + -1x) = 0


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

Simplifying
-10 + x = 0

Solving
-10 + x = 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 + x = 0 + 10

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

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

Simplifying
x = 10

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {10, 7}

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