9x^2-66x-121=0

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Solution for 9x^2-66x-121=0 equation: 


Simplifying
9x2 + -66x + -121 = 0

Reorder the terms:
-121 + -66x + 9x2 = 0

Solving
-121 + -66x + 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'.
-13.44444444 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '13.44444444' to each side of the equation.
-13.44444444 + -7.333333333x + 13.44444444 + x2 = 0 + 13.44444444

Reorder the terms:
-13.44444444 + 13.44444444 + -7.333333333x + x2 = 0 + 13.44444444

Combine like terms: -13.44444444 + 13.44444444 = 0.00000000
0.00000000 + -7.333333333x + x2 = 0 + 13.44444444
-7.333333333x + x2 = 0 + 13.44444444

Combine like terms: 0 + 13.44444444 = 13.44444444
-7.333333333x + x2 = 13.44444444

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = 13.44444444 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = 13.44444444 + 13.44444445

Combine like terms: 13.44444444 + 13.44444445 = 26.88888889
13.44444445 + -7.333333333x + x2 = 26.88888889

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 26.88888889

Calculate the square root of the right side: 5.185449729

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 5.185449729 and -5.185449729.


Subproblem 1
x + -3.666666667 = 5.185449729

Simplifying
x + -3.666666667 = 5.185449729

Reorder the terms:
-3.666666667 + x = 5.185449729

Solving
-3.666666667 + x = 5.185449729

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 5.185449729 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 5.185449729 + 3.666666667
x = 5.185449729 + 3.666666667

Combine like terms: 5.185449729 + 3.666666667 = 8.852116396
x = 8.852116396

Simplifying
x = 8.852116396


Subproblem 2
x + -3.666666667 = -5.185449729

Simplifying
x + -3.666666667 = -5.185449729

Reorder the terms:
-3.666666667 + x = -5.185449729

Solving
-3.666666667 + x = -5.185449729

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -5.185449729 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -5.185449729 + 3.666666667
x = -5.185449729 + 3.666666667

Combine like terms: -5.185449729 + 3.666666667 = -1.518783062
x = -1.518783062

Simplifying
x = -1.518783062


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.852116396, -1.518783062}

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