-9x^2+12x+17=0

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Solution for -9x^2+12x+17=0 equation: 


Simplifying
-9x2 + 12x + 17 = 0

Reorder the terms:
17 + 12x + -9x2 = 0

Solving
17 + 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'.
-1.888888889 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.888888889' to each side of the equation.
-1.888888889 + -1.333333333x + 1.888888889 + x2 = 0 + 1.888888889

Reorder the terms:
-1.888888889 + 1.888888889 + -1.333333333x + x2 = 0 + 1.888888889

Combine like terms: -1.888888889 + 1.888888889 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 1.888888889
-1.333333333x + x2 = 0 + 1.888888889

Combine like terms: 0 + 1.888888889 = 1.888888889
-1.333333333x + x2 = 1.888888889

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 = 1.888888889 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 1.888888889 + 0.4444444442

Combine like terms: 1.888888889 + 0.4444444442 = 2.3333333332
0.4444444442 + -1.333333333x + x2 = 2.3333333332

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 2.3333333332

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.527525232 and -1.527525232.


Subproblem 1
x + -0.6666666665 = 1.527525232

Simplifying
x + -0.6666666665 = 1.527525232

Reorder the terms:
-0.6666666665 + x = 1.527525232

Solving
-0.6666666665 + x = 1.527525232

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 = 1.527525232 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 1.527525232 + 0.6666666665
x = 1.527525232 + 0.6666666665

Combine like terms: 1.527525232 + 0.6666666665 = 2.1941918985
x = 2.1941918985

Simplifying
x = 2.1941918985


Subproblem 2
x + -0.6666666665 = -1.527525232

Simplifying
x + -0.6666666665 = -1.527525232

Reorder the terms:
-0.6666666665 + x = -1.527525232

Solving
-0.6666666665 + x = -1.527525232

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 = -1.527525232 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -1.527525232 + 0.6666666665
x = -1.527525232 + 0.6666666665

Combine like terms: -1.527525232 + 0.6666666665 = -0.8608585655
x = -0.8608585655

Simplifying
x = -0.8608585655


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1941918985, -0.8608585655}

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