9x^2-9x-15=0

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Solution for 9x^2-9x-15=0 equation: 


Simplifying
9x2 + -9x + -15 = 0

Reorder the terms:
-15 + -9x + 9x2 = 0

Solving
-15 + -9x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -3x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + -3x + 3x2 = 0

Solving
-5 + -3x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1x + x2 = 0 + 1.666666667
-1x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1x + x2 = 1.666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.666666667 + 0.25

Combine like terms: 1.666666667 + 0.25 = 1.916666667
0.25 + -1x + x2 = 1.916666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.384437311 and -1.384437311.


Subproblem 1
x + -0.5 = 1.384437311

Simplifying
x + -0.5 = 1.384437311

Reorder the terms:
-0.5 + x = 1.384437311

Solving
-0.5 + x = 1.384437311

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.384437311 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.384437311 + 0.5
x = 1.384437311 + 0.5

Combine like terms: 1.384437311 + 0.5 = 1.884437311
x = 1.884437311

Simplifying
x = 1.884437311


Subproblem 2
x + -0.5 = -1.384437311

Simplifying
x + -0.5 = -1.384437311

Reorder the terms:
-0.5 + x = -1.384437311

Solving
-0.5 + x = -1.384437311

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.384437311 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.384437311 + 0.5
x = -1.384437311 + 0.5

Combine like terms: -1.384437311 + 0.5 = -0.884437311
x = -0.884437311

Simplifying
x = -0.884437311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.884437311, -0.884437311}
Solution
x = {1.884437311, -0.884437311}

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