9x(x-81)=81

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Solution for 9x(x-81)=81 equation: 


Simplifying
9x(x + -81) = 81

Reorder the terms:
9x(-81 + x) = 81
(-81 * 9x + x * 9x) = 81
(-729x + 9x2) = 81

Solving
-729x + 9x2 = 81

Solving for variable 'x'.

Reorder the terms:
-81 + -729x + 9x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + -729x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-9 + -81x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-9 + -81x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -81x + x2 = 0

Solving
-9 + -81x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -81x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -81x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -81x + x2 = 0 + 9
-81x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-81x + x2 = 9

The x term is -81x.  Take half its coefficient (-40.5).
Square it (1640.25) and add it to both sides.

Add '1640.25' to each side of the equation.
-81x + 1640.25 + x2 = 9 + 1640.25

Reorder the terms:
1640.25 + -81x + x2 = 9 + 1640.25

Combine like terms: 9 + 1640.25 = 1649.25
1640.25 + -81x + x2 = 1649.25

Factor a perfect square on the left side:
(x + -40.5)(x + -40.5) = 1649.25

Calculate the square root of the right side: 40.610959112

Break this problem into two subproblems by setting 
(x + -40.5) equal to 40.610959112 and -40.610959112.


Subproblem 1
x + -40.5 = 40.610959112

Simplifying
x + -40.5 = 40.610959112

Reorder the terms:
-40.5 + x = 40.610959112

Solving
-40.5 + x = 40.610959112

Solving for variable 'x'.

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

Add '40.5' to each side of the equation.
-40.5 + 40.5 + x = 40.610959112 + 40.5

Combine like terms: -40.5 + 40.5 = 0.0
0.0 + x = 40.610959112 + 40.5
x = 40.610959112 + 40.5

Combine like terms: 40.610959112 + 40.5 = 81.110959112
x = 81.110959112

Simplifying
x = 81.110959112


Subproblem 2
x + -40.5 = -40.610959112

Simplifying
x + -40.5 = -40.610959112

Reorder the terms:
-40.5 + x = -40.610959112

Solving
-40.5 + x = -40.610959112

Solving for variable 'x'.

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

Add '40.5' to each side of the equation.
-40.5 + 40.5 + x = -40.610959112 + 40.5

Combine like terms: -40.5 + 40.5 = 0.0
0.0 + x = -40.610959112 + 40.5
x = -40.610959112 + 40.5

Combine like terms: -40.610959112 + 40.5 = -0.110959112
x = -0.110959112

Simplifying
x = -0.110959112


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {81.110959112, -0.110959112}
Solution
x = {81.110959112, -0.110959112}

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