9x^2-6x-44=0

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Solution for 9x^2-6x-44=0 equation: 


Simplifying
9x2 + -6x + -44 = 0

Reorder the terms:
-44 + -6x + 9x2 = 0

Solving
-44 + -6x + 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'.
-4.888888889 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '4.888888889' to each side of the equation.
-4.888888889 + -0.6666666667x + 4.888888889 + x2 = 0 + 4.888888889

Reorder the terms:
-4.888888889 + 4.888888889 + -0.6666666667x + x2 = 0 + 4.888888889

Combine like terms: -4.888888889 + 4.888888889 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 4.888888889
-0.6666666667x + x2 = 0 + 4.888888889

Combine like terms: 0 + 4.888888889 = 4.888888889
-0.6666666667x + x2 = 4.888888889

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 4.888888889 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 4.888888889 + 0.1111111112

Combine like terms: 4.888888889 + 0.1111111112 = 5.0000000002
0.1111111112 + -0.6666666667x + x2 = 5.0000000002

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 5.0000000002

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -0.3333333334 = 2.236067978

Simplifying
x + -0.3333333334 = 2.236067978

Reorder the terms:
-0.3333333334 + x = 2.236067978

Solving
-0.3333333334 + x = 2.236067978

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 2.236067978 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 2.236067978 + 0.3333333334
x = 2.236067978 + 0.3333333334

Combine like terms: 2.236067978 + 0.3333333334 = 2.5694013114
x = 2.5694013114

Simplifying
x = 2.5694013114


Subproblem 2
x + -0.3333333334 = -2.236067978

Simplifying
x + -0.3333333334 = -2.236067978

Reorder the terms:
-0.3333333334 + x = -2.236067978

Solving
-0.3333333334 + x = -2.236067978

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -2.236067978 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -2.236067978 + 0.3333333334
x = -2.236067978 + 0.3333333334

Combine like terms: -2.236067978 + 0.3333333334 = -1.9027346446
x = -1.9027346446

Simplifying
x = -1.9027346446


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5694013114, -1.9027346446}

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