9x^2-56x-729=0

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Solution for 9x^2-56x-729=0 equation: 


Simplifying
9x2 + -56x + -729 = 0

Reorder the terms:
-729 + -56x + 9x2 = 0

Solving
-729 + -56x + 9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-81 + -6.222222222x + x2 = 0

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -6.222222222x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -6.222222222x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -6.222222222x + x2 = 0 + 81
-6.222222222x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-6.222222222x + x2 = 81

The x term is -6.222222222x.  Take half its coefficient (-3.111111111).
Square it (9.679012345) and add it to both sides.

Add '9.679012345' to each side of the equation.
-6.222222222x + 9.679012345 + x2 = 81 + 9.679012345

Reorder the terms:
9.679012345 + -6.222222222x + x2 = 81 + 9.679012345

Combine like terms: 81 + 9.679012345 = 90.679012345
9.679012345 + -6.222222222x + x2 = 90.679012345

Factor a perfect square on the left side:
(x + -3.111111111)(x + -3.111111111) = 90.679012345

Calculate the square root of the right side: 9.522552827

Break this problem into two subproblems by setting 
(x + -3.111111111) equal to 9.522552827 and -9.522552827.


Subproblem 1
x + -3.111111111 = 9.522552827

Simplifying
x + -3.111111111 = 9.522552827

Reorder the terms:
-3.111111111 + x = 9.522552827

Solving
-3.111111111 + x = 9.522552827

Solving for variable 'x'.

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

Add '3.111111111' to each side of the equation.
-3.111111111 + 3.111111111 + x = 9.522552827 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + x = 9.522552827 + 3.111111111
x = 9.522552827 + 3.111111111

Combine like terms: 9.522552827 + 3.111111111 = 12.633663938
x = 12.633663938

Simplifying
x = 12.633663938


Subproblem 2
x + -3.111111111 = -9.522552827

Simplifying
x + -3.111111111 = -9.522552827

Reorder the terms:
-3.111111111 + x = -9.522552827

Solving
-3.111111111 + x = -9.522552827

Solving for variable 'x'.

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

Add '3.111111111' to each side of the equation.
-3.111111111 + 3.111111111 + x = -9.522552827 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + x = -9.522552827 + 3.111111111
x = -9.522552827 + 3.111111111

Combine like terms: -9.522552827 + 3.111111111 = -6.411441716
x = -6.411441716

Simplifying
x = -6.411441716


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.633663938, -6.411441716}

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