9x^2-12x-113=0

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Solution for 9x^2-12x-113=0 equation: 


Simplifying
9x2 + -12x + -113 = 0

Reorder the terms:
-113 + -12x + 9x2 = 0

Solving
-113 + -12x + 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'.
-12.55555556 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '12.55555556' to each side of the equation.
-12.55555556 + -1.333333333x + 12.55555556 + x2 = 0 + 12.55555556

Reorder the terms:
-12.55555556 + 12.55555556 + -1.333333333x + x2 = 0 + 12.55555556

Combine like terms: -12.55555556 + 12.55555556 = 0.00000000
0.00000000 + -1.333333333x + x2 = 0 + 12.55555556
-1.333333333x + x2 = 0 + 12.55555556

Combine like terms: 0 + 12.55555556 = 12.55555556
-1.333333333x + x2 = 12.55555556

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 12.55555556 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 12.55555556 + 0.4444444442

Combine like terms: 12.55555556 + 0.4444444442 = 13.0000000042
0.4444444442 + -1.333333333x + x2 = 13.0000000042

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 13.0000000042

Calculate the square root of the right side: 3.605551276

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 3.605551276 and -3.605551276.


Subproblem 1
x + -0.6666666665 = 3.605551276

Simplifying
x + -0.6666666665 = 3.605551276

Reorder the terms:
-0.6666666665 + x = 3.605551276

Solving
-0.6666666665 + x = 3.605551276

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 3.605551276 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 3.605551276 + 0.6666666665
x = 3.605551276 + 0.6666666665

Combine like terms: 3.605551276 + 0.6666666665 = 4.2722179425
x = 4.2722179425

Simplifying
x = 4.2722179425


Subproblem 2
x + -0.6666666665 = -3.605551276

Simplifying
x + -0.6666666665 = -3.605551276

Reorder the terms:
-0.6666666665 + x = -3.605551276

Solving
-0.6666666665 + x = -3.605551276

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -3.605551276 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -3.605551276 + 0.6666666665
x = -3.605551276 + 0.6666666665

Combine like terms: -3.605551276 + 0.6666666665 = -2.9388846095
x = -2.9388846095

Simplifying
x = -2.9388846095


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.2722179425, -2.9388846095}

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