9x^2-12x-35=0

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Solution for 9x^2-12x-35=0 equation: 


Simplifying
9x2 + -12x + -35 = 0

Reorder the terms:
-35 + -12x + 9x2 = 0

Solving
-35 + -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'.
-3.888888889 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '3.888888889' to each side of the equation.
-3.888888889 + -1.333333333x + 3.888888889 + x2 = 0 + 3.888888889

Reorder the terms:
-3.888888889 + 3.888888889 + -1.333333333x + x2 = 0 + 3.888888889

Combine like terms: -3.888888889 + 3.888888889 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 3.888888889
-1.333333333x + x2 = 0 + 3.888888889

Combine like terms: 0 + 3.888888889 = 3.888888889
-1.333333333x + x2 = 3.888888889

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 = 3.888888889 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 3.888888889 + 0.4444444442

Combine like terms: 3.888888889 + 0.4444444442 = 4.3333333332
0.4444444442 + -1.333333333x + x2 = 4.3333333332

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 4.3333333332

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.081665999 and -2.081665999.


Subproblem 1
x + -0.6666666665 = 2.081665999

Simplifying
x + -0.6666666665 = 2.081665999

Reorder the terms:
-0.6666666665 + x = 2.081665999

Solving
-0.6666666665 + x = 2.081665999

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 = 2.081665999 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 2.081665999 + 0.6666666665
x = 2.081665999 + 0.6666666665

Combine like terms: 2.081665999 + 0.6666666665 = 2.7483326655
x = 2.7483326655

Simplifying
x = 2.7483326655


Subproblem 2
x + -0.6666666665 = -2.081665999

Simplifying
x + -0.6666666665 = -2.081665999

Reorder the terms:
-0.6666666665 + x = -2.081665999

Solving
-0.6666666665 + x = -2.081665999

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 = -2.081665999 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -2.081665999 + 0.6666666665
x = -2.081665999 + 0.6666666665

Combine like terms: -2.081665999 + 0.6666666665 = -1.4149993325
x = -1.4149993325

Simplifying
x = -1.4149993325


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.7483326655, -1.4149993325}

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