9x^2+138x-189=0

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Solution for 9x^2+138x-189=0 equation: 


Simplifying
9x2 + 138x + -189 = 0

Reorder the terms:
-189 + 138x + 9x2 = 0

Solving
-189 + 138x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-63 + 46x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-63 + 46x + 3x2)' equal to zero and attempt to solve:

Simplifying
-63 + 46x + 3x2 = 0

Solving
-63 + 46x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-21 + 15.33333333x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 15.33333333x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 15.33333333x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 15.33333333x + x2 = 0 + 21
15.33333333x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
15.33333333x + x2 = 21

The x term is 15.33333333x.  Take half its coefficient (7.666666665).
Square it (58.77777775) and add it to both sides.

Add '58.77777775' to each side of the equation.
15.33333333x + 58.77777775 + x2 = 21 + 58.77777775

Reorder the terms:
58.77777775 + 15.33333333x + x2 = 21 + 58.77777775

Combine like terms: 21 + 58.77777775 = 79.77777775
58.77777775 + 15.33333333x + x2 = 79.77777775

Factor a perfect square on the left side:
(x + 7.666666665)(x + 7.666666665) = 79.77777775

Calculate the square root of the right side: 8.93184067

Break this problem into two subproblems by setting 
(x + 7.666666665) equal to 8.93184067 and -8.93184067.


Subproblem 1
x + 7.666666665 = 8.93184067

Simplifying
x + 7.666666665 = 8.93184067

Reorder the terms:
7.666666665 + x = 8.93184067

Solving
7.666666665 + x = 8.93184067

Solving for variable 'x'.

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

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = 8.93184067 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = 8.93184067 + -7.666666665
x = 8.93184067 + -7.666666665

Combine like terms: 8.93184067 + -7.666666665 = 1.265174005
x = 1.265174005

Simplifying
x = 1.265174005


Subproblem 2
x + 7.666666665 = -8.93184067

Simplifying
x + 7.666666665 = -8.93184067

Reorder the terms:
7.666666665 + x = -8.93184067

Solving
7.666666665 + x = -8.93184067

Solving for variable 'x'.

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

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = -8.93184067 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = -8.93184067 + -7.666666665
x = -8.93184067 + -7.666666665

Combine like terms: -8.93184067 + -7.666666665 = -16.598507335
x = -16.598507335

Simplifying
x = -16.598507335


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.265174005, -16.598507335}
Solution
x = {1.265174005, -16.598507335}

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